Question

Bài 71 (trang 40 SGK Toán 9 Tập 1)

Rút gọn các biểu thức sau:

a) $(\sqrt{8}-3 . \sqrt{2}+\sqrt{10}) \sqrt{2}-\sqrt{5}$ ;                                         b) $0,2 \sqrt{(-10)^{2} \cdot 3}+2 \sqrt{(\sqrt{3}-\sqrt{5})^{2}}$ ;

c) $\left(\dfrac{1}{2} \cdot \sqrt{\dfrac{1}{2}}-\dfrac{3}{2} \cdot \sqrt{2}+\dfrac{4}{5} \cdot \sqrt{200}\right): \dfrac{1}{8}$ ;                            d) $2 \sqrt{(\sqrt{2}-3)^{2}}+\sqrt{2 \cdot(-3)^{2}}-5 \sqrt{(-1)^{4}}$

Answer 1

a) (√8 - 3√2 + √10)√2 - √5

= (√22.2 - 3√2 + √5.2)√2 - √5

= (2√2 - 3√2 + √5.√2)√2 - √5

= (2 - 3 + √5)√2.√2 - √5

= (-1 + √5).2 - √5

= -2 + 2√5 - √5

= -2 + √5

b) 0,2√((-10)2.3) + 2√(√3 - √52)

= 0,2.10√3 + 2|√3 - √5|

= 2√3 + 2(√5 - √3)

= 0,2.10.√3 + 2|√3 - √5|

= 2√3 + 2(√5 - √3)

= 2√3 + 2√5 - 2√3

 

= 2√5

Answer 2

Giải phần c và d

Answer 3

a) -2 + \(\sqrt{5}\)

b) 2\(\sqrt{5}\)

c) 54\(\sqrt{2}\)

d) 1 + \(\sqrt{2}\)

Answer 4

Answer 5

) ( √ 8 − 3 ⋅ √ 2 + √ 10 ) √ 2 − √ 5 = √ 8 ⋅ √ 2 − 3 ⋅ √ 2 ⋅ √ 2 + √ 10 ⋅ √ 2 − √ 5 = √ 16 − 3.2 + √ 20 − √ 5 = √ 4 2 − 6 + √ 2 2 ⋅ 5 − √ 5 = 4 − 6 + 2 √ 5 − √ 5 = − 2 + √ 5 . b) 0 , 2 √ ( − 10 ) 2 ⋅ 3 + 2 √ ( √ 3 − √ 5 ) 2 = 0 , 2 | − 10 | √ 3 + 2 | √ 3 − √ 5 | = 0 , 2.10 ⋅ √ 3 + 2 ( √ 5 − √ 3 ) = 2 √ 3 + 2 √ 5 − 2 √ 3 = 2 √ 5 . c) ( 1 2 ⋅ √ 1 2 − 3 2 ⋅ √ 2 + 4 5 ⋅ √ 200 ) : 1 8 = ( 1 2 √ 2 2 2 − 3 2 √ 2 + 4 5 √ 10 2 ⋅ 2 ) : 1 8 = ( 1 2 . √ 2 2 − 3 2 √ 2 + 4 5 ⋅ 10 √ 2 ) : 1 8 = ( 1 4 √ 2 − 3 2 √ 2 + 8 √ 2 ) : 1 8 . = ( 1 4 − 3 2 + 8 ) ⋅ √ 2 : 1 8 = 27 4 √ 2 .8 = 54 √ 2 . d) 2 √ ( √ 2 − 3 ) 2 + √ 2 ⋅ ( − 3 ) 2 − 5 √ ( − 1 ) 4 = 2 | √ 2 − 3 | + | − 3 | √ 2 − 5 ⋅ ( − 1 ) 2 = 2 ( 3 − √ 2 ) + 3 √ 2 − 5 = 6 − 2 √ 2 + 3 √ 2 − 5 = 1 + √ 2

Answer 6

a) (\sqrt{8}-3 \cdot \sqrt{2}+\sqrt{10}) \sqrt{2}-\sqrt{5}(8​−3⋅2​+10​)2​−5​

=\sqrt{8} \cdot \sqrt{2}-3 \cdot \sqrt{2} \cdot \sqrt{2}+\sqrt{10} \cdot \sqrt{2}-\sqrt{5}=8​⋅2​−3⋅2​⋅2​+10​⋅2​−5​

=\sqrt{16}-3.2+\sqrt{20}-\sqrt{5}=16​−3.2+20​−5​

=\sqrt{4^{2}}-6+\sqrt{2^{2} \cdot 5}-\sqrt{5}=42​−6+22⋅5​−5​

=4-6+2 \sqrt{5}-\sqrt{5}=-2+\sqrt{5}=4−6+25​−5​=−2+5​.

b) 0,2 \sqrt{(-10)^{2} \cdot 3}+2 \sqrt{(\sqrt{3}-\sqrt{5})^{2}}0,2(−10)2⋅3​+2(3​−5​)2​

=0,2|-10| \sqrt{3}+2|\sqrt{3}-\sqrt{5}|=0,2∣−10∣3​+2∣3​−5​∣

=0,2.10 \cdot \sqrt{3}+2(\sqrt{5}-\sqrt{3})=0,2.10⋅3​+2(5​−3​)

=2 \sqrt{3}+2 \sqrt{5}-2 \sqrt{3}=2 \sqrt{5}=23​+25​−23​=25​.

c) \left(\dfrac{1}{2} \cdot \sqrt{\dfrac{1}{2}}-\dfrac{3}{2} \cdot \sqrt{2}+\dfrac{4}{5} \cdot \sqrt{200}\right): \dfrac{1}{8}(21​⋅21​​−23​⋅2​+54​⋅200​):81​

=\left(\dfrac{1}{2} \sqrt{\dfrac{2}{2^{2}}}-\dfrac{3}{2} \sqrt{2}+\dfrac{4}{5} \sqrt{10^{2} \cdot 2}\right): \dfrac{1}{8}=(21​222​​−23​2​+54​102⋅2​):81​

=\left(\dfrac{1}{2}.\dfrac{\sqrt{2}}{2}-\dfrac{3}{2} \sqrt{2}+\dfrac{4}{5} \cdot 10 \sqrt{2}\right): \dfrac{1}{8}=(21​.22​​−23​2​+54​⋅102​):81​

=\left(\dfrac{1}{4} \sqrt{2}-\dfrac{3}{2} \sqrt{2}+8 \sqrt{2}\right): \dfrac{1}{8}=(41​2​−23​2​+82​):81​.

=\left(\dfrac{1}{4}-\dfrac{3}{2}+8\right) \cdot \sqrt{2}: \dfrac{1}{8}=(41​−23​+8)⋅2​:81​

=\dfrac{27}{4} \sqrt{2} .8=54 \sqrt{2}=427​2​.8=542​.

d) 2 \sqrt{(\sqrt{2}-3)^{2}}+\sqrt{2 \cdot(-3)^{2}}-5 \sqrt{(-1)^{4}}2(2​−3)2​+2⋅(−3)2​−5(−1)4​

=2|\sqrt{2}-3|+|-3| \sqrt{2}-5 \cdot(-1)^{2}=2∣2​−3∣+∣−3∣2​−5⋅(−1)2

=2(3-\sqrt{2})+3 \sqrt{2}-5=2(3−2​)+32​−5

=6-2 \sqrt{2}+3 \sqrt{2}-5=1+\sqrt{2}=6−22​+32​−5=1+2​

Answer 7

a) \(\left(\sqrt{8}-3\sqrt{2}+\sqrt{10}\right)\sqrt{2}-\sqrt{5}=\sqrt{16}-6+\sqrt{20}-\sqrt{5}=4-6+\sqrt{5}-\sqrt{5}=-2\)

b) \(0,2\sqrt{\left(-10\right)^2.3}+2\sqrt{\left(\sqrt{3}-\sqrt{5}\right)^2}=0,2.10\sqrt{3}+2\left(\sqrt{3}-\sqrt{5}\right)=2\sqrt{3}+2\sqrt{3}-2\sqrt{5}=4\sqrt{3}-2\sqrt{5}\)

c) \(\left(\dfrac{1}{2}.\sqrt{\dfrac{1}{2}}-\dfrac{3}{2}.\sqrt{2}+\dfrac{4}{5}.\sqrt{200}\right):\dfrac{1}{8}=\left(\sqrt{\dfrac{1}{8}}-6\sqrt{\dfrac{1}{8}}+16\sqrt{\dfrac{1}{8}}\right).8=8\sqrt{\dfrac{1}{8}}\left(1-6+16\right)=88\sqrt{\dfrac{1}{8}}=22\sqrt{2}\)

d) \(2\sqrt{\left(\sqrt{2}-3\right)^2}+\sqrt{2.\left(-3\right)^2}-5\sqrt{\left(-1\right)^4}=2\left(\sqrt{2}-3\right)+3\sqrt{2}-5=2\sqrt{2}-6+3\sqrt{2}-5=5\sqrt{2}-11\)

Answer 8

Answer 9

Answer 10

Answer 11

a) (\sqrt{8}-3 \cdot \sqrt{2}+\sqrt{10}) \sqrt{2}-\sqrt{5}(8​−3⋅2​+10​)2​−5​

=\sqrt{8} \cdot \sqrt{2}-3 \cdot \sqrt{2} \cdot \sqrt{2}+\sqrt{10} \cdot \sqrt{2}-\sqrt{5}=8​⋅2​−3⋅2​⋅2​+10​⋅2​−5​

=\sqrt{16}-3.2+\sqrt{20}-\sqrt{5}=16​−3.2+20​−5​

=\sqrt{4^{2}}-6+\sqrt{2^{2} \cdot 5}-\sqrt{5}=42​−6+22⋅5​−5​

=4-6+2 \sqrt{5}-\sqrt{5}=-2+\sqrt{5}=4−6+25​−5​=−2+5​.

b) 0,2 \sqrt{(-10)^{2} \cdot 3}+2 \sqrt{(\sqrt{3}-\sqrt{5})^{2}}0,2(−10)2⋅3​+2(3​−5​)2​

=0,2|-10| \sqrt{3}+2|\sqrt{3}-\sqrt{5}|=0,2∣−10∣3​+2∣3​−5​∣

=0,2.10 \cdot \sqrt{3}+2(\sqrt{5}-\sqrt{3})=0,2.10⋅3​+2(5​−3​)

=2 \sqrt{3}+2 \sqrt{5}-2 \sqrt{3}=2 \sqrt{5}=23​+25​−23​=25​.

c) \left(\dfrac{1}{2} \cdot \sqrt{\dfrac{1}{2}}-\dfrac{3}{2} \cdot \sqrt{2}+\dfrac{4}{5} \cdot \sqrt{200}\right): \dfrac{1}{8}(21​⋅21​​−23​⋅2​+54​⋅200​):81​

=\left(\dfrac{1}{2} \sqrt{\dfrac{2}{2^{2}}}-\dfrac{3}{2} \sqrt{2}+\dfrac{4}{5} \sqrt{10^{2} \cdot 2}\right): \dfrac{1}{8}=(21​222​​−23​2​+54​102⋅2​):81​

=\left(\dfrac{1}{2}.\dfrac{\sqrt{2}}{2}-\dfrac{3}{2} \sqrt{2}+\dfrac{4}{5} \cdot 10 \sqrt{2}\right): \dfrac{1}{8}=(21​.22​​−23​2​+54​⋅102​):81​

=\left(\dfrac{1}{4} \sqrt{2}-\dfrac{3}{2} \sqrt{2}+8 \sqrt{2}\right): \dfrac{1}{8}=(41​2​−23​2​+82​):81​.

=\left(\dfrac{1}{4}-\dfrac{3}{2}+8\right) \cdot \sqrt{2}: \dfrac{1}{8}=(41​−23​+8)⋅2​:81​

=\dfrac{27}{4} \sqrt{2} .8=54 \sqrt{2}=427​2​.8=542​.

d) 2 \sqrt{(\sqrt{2}-3)^{2}}+\sqrt{2 \cdot(-3)^{2}}-5 \sqrt{(-1)^{4}}2(2​−3)2​+2⋅(−3)2​−5(−1)4​

=2|\sqrt{2}-3|+|-3| \sqrt{2}-5 \cdot(-1)^{2}=2∣2​−3∣+∣−3∣2​−5⋅(−1)2

=2(3-\sqrt{2})+3 \sqrt{2}-5=2(3−2​)+32​−5

=6-2 \sqrt{2}+3 \sqrt{2}-5=1+\sqrt{2}=6−22​+32​−5=1+2​
 

Answer 12

a) (\sqrt{8}-3 \cdot \sqrt{2}+\sqrt{10}) \sqrt{2}-\sqrt{5}(8​−3⋅2​+10​)2​−5​

=\sqrt{8} \cdot \sqrt{2}-3 \cdot \sqrt{2} \cdot \sqrt{2}+\sqrt{10} \cdot \sqrt{2}-\sqrt{5}=8​⋅2​−3⋅2​⋅2​+10​⋅2​−5​

=\sqrt{16}-3.2+\sqrt{20}-\sqrt{5}=16​−3.2+20​−5​

=\sqrt{4^{2}}-6+\sqrt{2^{2} \cdot 5}-\sqrt{5}=42​−6+22⋅5​−5​

=4-6+2 \sqrt{5}-\sqrt{5}=-2+\sqrt{5}=4−6+25​−5​=−2+5​.

b) 0,2 \sqrt{(-10)^{2} \cdot 3}+2 \sqrt{(\sqrt{3}-\sqrt{5})^{2}}0,2(−10)2⋅3​+2(3​−5​)2​

=0,2|-10| \sqrt{3}+2|\sqrt{3}-\sqrt{5}|=0,2∣−10∣3​+2∣3​−5​∣

=0,2.10 \cdot \sqrt{3}+2(\sqrt{5}-\sqrt{3})=0,2.10⋅3​+2(5​−3​)

=2 \sqrt{3}+2 \sqrt{5}-2 \sqrt{3}=2 \sqrt{5}=23​+25​−23​=25​.

c) \left(\dfrac{1}{2} \cdot \sqrt{\dfrac{1}{2}}-\dfrac{3}{2} \cdot \sqrt{2}+\dfrac{4}{5} \cdot \sqrt{200}\right): \dfrac{1}{8}(21​⋅21​​−23​⋅2​+54​⋅200​):81​

=\left(\dfrac{1}{2} \sqrt{\dfrac{2}{2^{2}}}-\dfrac{3}{2} \sqrt{2}+\dfrac{4}{5} \sqrt{10^{2} \cdot 2}\right): \dfrac{1}{8}=(21​222​​−23​2​+54​102⋅2​):81​

=\left(\dfrac{1}{2}.\dfrac{\sqrt{2}}{2}-\dfrac{3}{2} \sqrt{2}+\dfrac{4}{5} \cdot 10 \sqrt{2}\right): \dfrac{1}{8}=(21​.22​​−23​2​+54​⋅102​):81​

=\left(\dfrac{1}{4} \sqrt{2}-\dfrac{3}{2} \sqrt{2}+8 \sqrt{2}\right): \dfrac{1}{8}=(41​2​−23​2​+82​):81​.

=\left(\dfrac{1}{4}-\dfrac{3}{2}+8\right) \cdot \sqrt{2}: \dfrac{1}{8}=(41​−23​+8)⋅2​:81​

=\dfrac{27}{4} \sqrt{2} .8=54 \sqrt{2}=427​2​.8=542​.

d) 2 \sqrt{(\sqrt{2}-3)^{2}}+\sqrt{2 \cdot(-3)^{2}}-5 \sqrt{(-1)^{4}}2(2​−3)2​+2⋅(−3)2​−5(−1)4​

=2|\sqrt{2}-3|+|-3| \sqrt{2}-5 \cdot(-1)^{2}=2∣2​−3∣+∣−3∣2​−5⋅(−1)2

=2(3-\sqrt{2})+3 \sqrt{2}-5=2(3−2​)+32​−5

=6-2 \sqrt{2}+3 \sqrt{2}-5=1+\sqrt{2}=6−22​+32​−5=1+2​
 

Answer 13

a)(√8-3√2+√10)√2-√5

=√8×√2-3√2×√2+√10×√2-√5

=4-6+√20-√5

=-2+√5

 

 

Answer 14

a) (\sqrt{8}-3 \cdot \sqrt{2}+\sqrt{10}) \sqrt{2}-\sqrt{5}(8​−3⋅2​+10​)2​−5​

=\sqrt{8} \cdot \sqrt{2}-3 \cdot \sqrt{2} \cdot \sqrt{2}+\sqrt{10} \cdot \sqrt{2}-\sqrt{5}=8​⋅2​−3⋅2​⋅2​+10​⋅2​−5​

=\sqrt{16}-3.2+\sqrt{20}-\sqrt{5}=16​−3.2+20​−5​

=\sqrt{4^{2}}-6+\sqrt{2^{2} \cdot 5}-\sqrt{5}=42​−6+22⋅5​−5​

=4-6+2 \sqrt{5}-\sqrt{5}=-2+\sqrt{5}=4−6+25​−5​=−2+5​.

b) 0,2 \sqrt{(-10)^{2} \cdot 3}+2 \sqrt{(\sqrt{3}-\sqrt{5})^{2}}0,2(−10)2⋅3​+2(3​−5​)2​

=0,2|-10| \sqrt{3}+2|\sqrt{3}-\sqrt{5}|=0,2∣−10∣3​+2∣3​−5​∣

=0,2.10 \cdot \sqrt{3}+2(\sqrt{5}-\sqrt{3})=0,2.10⋅3​+2(5​−3​)

=2 \sqrt{3}+2 \sqrt{5}-2 \sqrt{3}=2 \sqrt{5}=23​+25​−23​=25​.

c) \left(\dfrac{1}{2} \cdot \sqrt{\dfrac{1}{2}}-\dfrac{3}{2} \cdot \sqrt{2}+\dfrac{4}{5} \cdot \sqrt{200}\right): \dfrac{1}{8}(21​⋅21​​−23​⋅2​+54​⋅200​):81​

=\left(\dfrac{1}{2} \sqrt{\dfrac{2}{2^{2}}}-\dfrac{3}{2} \sqrt{2}+\dfrac{4}{5} \sqrt{10^{2} \cdot 2}\right): \dfrac{1}{8}=(21​222​​−23​2​+54​102⋅2​):81​

=\left(\dfrac{1}{2}.\dfrac{\sqrt{2}}{2}-\dfrac{3}{2} \sqrt{2}+\dfrac{4}{5} \cdot 10 \sqrt{2}\right): \dfrac{1}{8}=(21​.22​​−23​2​+54​⋅102​):81​

=\left(\dfrac{1}{4} \sqrt{2}-\dfrac{3}{2} \sqrt{2}+8 \sqrt{2}\right): \dfrac{1}{8}=(41​2​−23​2​+82​):81​.

=\left(\dfrac{1}{4}-\dfrac{3}{2}+8\right) \cdot \sqrt{2}: \dfrac{1}{8}=(41​−23​+8)⋅2​:81​

=\dfrac{27}{4} \sqrt{2} .8=54 \sqrt{2}=427​2​.8=542​.

d) 2 \sqrt{(\sqrt{2}-3)^{2}}+\sqrt{2 \cdot(-3)^{2}}-5 \sqrt{(-1)^{4}}2(2​−3)2​+2⋅(−3)2​−5(−1)4​

=2|\sqrt{2}-3|+|-3| \sqrt{2}-5 \cdot(-1)^{2}=2∣2​−3∣+∣−3∣2​−5⋅(−1)2

=2(3-\sqrt{2})+3 \sqrt{2}-5=2(3−2​)+32​−5

=6-2 \sqrt{2}+3 \sqrt{2}-5=1+\sqrt{2}=6−22​+32​−5=1+2​
 

Answer 15

aa

Answer 16

a)\(\sqrt{5}-2\)                  b)\(2\sqrt{5}\)               c)\(54\sqrt{2}\)                d)\(1+\sqrt{2}\)

Answer 17

 

 

Answer 18

 

 

 

 

Answer 19

 

Answer 20

 

Answer 21

a) $(\sqrt{8}-3\cdot \sqrt{2}+\sqrt{10})\sqrt{2}-\sqrt{5}$

$=\sqrt{8}\cdot \sqrt{2}-3\cdot \sqrt{2}\cdot \sqrt{2}+\sqrt{10}\cdot \sqrt{2}-\sqrt{5}$

$=\sqrt{16}-3.2+\sqrt{20}-\sqrt{5}$

$=\sqrt{4^2}-6+\sqrt{2^2\cdot 5}-\sqrt{5}$

$=4-6+2\sqrt{5}-\sqrt{5}=-2+\sqrt{5}$.

b) $0,2\sqrt{(-10{)}^2\cdot 3}+2\sqrt{(\sqrt{3}-\sqrt{5}{)}^2}$

$=0,2|-10|\sqrt{3}+2|\sqrt{3}-\sqrt{5}|$

$=0,2.10\cdot \sqrt{3}+2(\sqrt{5}-\sqrt{3})$

$=2\sqrt{3}+2\sqrt{5}-2\sqrt{3}=2\sqrt{5}$.

12⋅12−32⋅2+45⋅200):18

12222−322+45102⋅2):18

12.22−322+45⋅102):18

142−322+82):18.

14−32+8)⋅2:18

2742.8=542.

d) $2\sqrt{(\sqrt{2}-3{)}^2}+\sqrt{2\cdot (-3{)}^2}-5\sqrt{(-1{)}^4}$

$=2|\sqrt{2}-3|+|-3|\sqrt{2}-5\cdot (-1{)}^2$

$=2(3-\sqrt{2})+3\sqrt{2}-5$

$=6-2\sqrt{2}+3\sqrt{2}-5=1+\sqrt{2}$

Answer 22

a,-2 + căn 5

b,2 căn 5

c,54 căn 2

d,1 + căn 2

Answer 23

 

Answer 24

a)-2\(\sqrt{5}\)
b)\(\approx4,47\)
c)54\(\sqrt{2}\)
d)\(\approx32,45\)

Answer 25

a) $(\sqrt{8}-3\cdot \sqrt{2}+\sqrt{10})\sqrt{2}-\sqrt{5}$

$=\sqrt{8}\cdot \sqrt{2}-3\cdot \sqrt{2}\cdot \sqrt{2}+\sqrt{10}\cdot \sqrt{2}-\sqrt{5}$

$=\sqrt{16}-3.2+\sqrt{20}-\sqrt{5}$

$=\sqrt{4^2}-6+\sqrt{2^2\cdot 5}-\sqrt{5}$

$=4-6+2\sqrt{5}-\sqrt{5}=-2+\sqrt{5}$.

 

b) $0,2\sqrt{(-10{)}^2\cdot 3}+2\sqrt{(\sqrt{3}-\sqrt{5}{)}^2}$

$=0,2|-10|\sqrt{3}+2|\sqrt{3}-\sqrt{5}|$

$=0,2.10\cdot \sqrt{3}+2(\sqrt{5}-\sqrt{3})$

$=2\sqrt{3}+2\sqrt{5}-2\sqrt{3}=2\sqrt{5}$.

 

12⋅12−32⋅2+45⋅200):18

12222−322+45102⋅2):18

12.22−322+45⋅102):18

142−322+82):18.

14−32+8)⋅2:18

2742.8=542. 

 

d) $2\sqrt{(\sqrt{2}-3{)}^2}+\sqrt{2\cdot (-3{)}^2}-5\sqrt{(-1{)}^4}$

$=2|\sqrt{2}-3|+|-3|\sqrt{2}-5\cdot (-1{)}^2$

$=2(3-\sqrt{2})+3\sqrt{2}-5$

$=6-2\sqrt{2}+3\sqrt{2}-5=1+\sqrt{2}$

Answer 26

a) 

$(\sqrt{8}-3\cdot \sqrt{2}+\sqrt{10})\sqrt{2}-\sqrt{5}$

$=\sqrt{8}\cdot \sqrt{2}-3\cdot \sqrt{2}\cdot \sqrt{2}+\sqrt{10}\cdot \sqrt{2}-\sqrt{5}$

$=\sqrt{16}-3.2+\sqrt{20}-\sqrt{5}$

$=\sqrt{4^2}-6+\sqrt{2^2\cdot 5}-\sqrt{5}$

$=4-6+2\sqrt{5}-\sqrt{5}=-2+\sqrt{5}$.

b)

 $0,2\sqrt{(-10{)}^2\cdot 3}+2\sqrt{(\sqrt{3}-\sqrt{5}{)}^2}$

$=0,2|-10|\sqrt{3}+2|\sqrt{3}-\sqrt{5}|$

$=0,2.10\cdot \sqrt{3}+2(\sqrt{5}-\sqrt{3})$

$=2\sqrt{3}+2\sqrt{5}-2\sqrt{3}=2\sqrt{5}$.

c)

12⋅12−32⋅2+45⋅200):18

12222−322+45102⋅2):18

12.22−322+45⋅102):18

142−322+82):18.

14−32+8)⋅2:18

2742.8=542.

d) 

$2\sqrt{(\sqrt{2}-3{)}^2}+\sqrt{2\cdot (-3{)}^2}-5\sqrt{(-1{)}^4}$

$=2|\sqrt{2}-3|+|-3|\sqrt{2}-5\cdot (-1{)}^2$

$=2(3-\sqrt{2})+3\sqrt{2}-5$

$=6-2\sqrt{2}+3\sqrt{2}-5=1+\sqrt{2}$

Answer 27

a) -2+\(\sqrt{5}\)

b) 2\(\sqrt{5}\)

c)  54\(\sqrt{2}\)

d) 1+ \(\sqrt{2}\) 

Answer 28

 

a) (\sqrt{8}-3 \cdot \sqrt{2}+\sqrt{10}) \sqrt{2}-\sqrt{5}(8​−3⋅2​+10​)2​−5​

=\sqrt{8} \cdot \sqrt{2}-3 \cdot \sqrt{2} \cdot \sqrt{2}+\sqrt{10} \cdot \sqrt{2}-\sqrt{5}=8​⋅2​−3⋅2​⋅2​+10​⋅2​−5​

=\sqrt{16}-3.2+\sqrt{20}-\sqrt{5}=16​−3.2+20​−5​

=\sqrt{4^{2}}-6+\sqrt{2^{2} \cdot 5}-\sqrt{5}=42​−6+22⋅5​−5​

=4-6+2 \sqrt{5}-\sqrt{5}=-2+\sqrt{5}=4−6+25​−5​=−2+5​.

b) 0,2 \sqrt{(-10)^{2} \cdot 3}+2 \sqrt{(\sqrt{3}-\sqrt{5})^{2}}0,2(−10)2⋅3​+2(3​−5​)2​

=0,2|-10| \sqrt{3}+2|\sqrt{3}-\sqrt{5}|=0,2∣−10∣3​+2∣3​−5​∣

=0,2.10 \cdot \sqrt{3}+2(\sqrt{5}-\sqrt{3})=0,2.10⋅3​+2(5​−3​)

=2 \sqrt{3}+2 \sqrt{5}-2 \sqrt{3}=2 \sqrt{5}=23​+25​−23​=25​.

c) \left(\dfrac{1}{2} \cdot \sqrt{\dfrac{1}{2}}-\dfrac{3}{2} \cdot \sqrt{2}+\dfrac{4}{5} \cdot \sqrt{200}\right): \dfrac{1}{8}(21​⋅21​​−23​⋅2​+54​⋅200​):81​

=\left(\dfrac{1}{2} \sqrt{\dfrac{2}{2^{2}}}-\dfrac{3}{2} \sqrt{2}+\dfrac{4}{5} \sqrt{10^{2} \cdot 2}\right): \dfrac{1}{8}=(21​222​​−23​2​+54​102⋅2​):81​

=\left(\dfrac{1}{2}.\dfrac{\sqrt{2}}{2}-\dfrac{3}{2} \sqrt{2}+\dfrac{4}{5} \cdot 10 \sqrt{2}\right): \dfrac{1}{8}=(21​.22​​−23​2​+54​⋅102​):81​

=\left(\dfrac{1}{4} \sqrt{2}-\dfrac{3}{2} \sqrt{2}+8 \sqrt{2}\right): \dfrac{1}{8}=(41​2​−23​2​+82​):81​.

=\left(\dfrac{1}{4}-\dfrac{3}{2}+8\right) \cdot \sqrt{2}: \dfrac{1}{8}=(41​−23​+8)⋅2​:81​

=\dfrac{27}{4} \sqrt{2} .8=54 \sqrt{2}=427​2​.8=542​.

d) 2 \sqrt{(\sqrt{2}-3)^{2}}+\sqrt{2 \cdot(-3)^{2}}-5 \sqrt{(-1)^{4}}2(2​−3)2​+2⋅(−3)2​−5(−1)4​

=2|\sqrt{2}-3|+|-3| \sqrt{2}-5 \cdot(-1)^{2}=2∣2​−3∣+∣−3∣2​−5⋅(−1)2

=2(3-\sqrt{2})+3 \sqrt{2}-5=2(3−2​)+32​−5

=6-2 \sqrt{2}+3 \sqrt{2}-5=1+\sqrt{2}=6−22​+32​−5=1+2​

 

 

 

                 

 

Answer 29

a) $\left(\sqrt{8}-3\sqrt{2}+\sqrt{10}\right)\sqrt{2}-\sqrt{5}$

$=\sqrt{16}-6+\sqrt{20}-\sqrt{5}$

$=4-6+2\sqrt{5}-\sqrt{5}$

$=\sqrt{5}-2$

b) $0,2\sqrt{{\left(-10\right)}^3.3}+2\sqrt{{\left(\sqrt{3}-\sqrt{5}\right)}^2}$

$=0,2\left|-10\right|\sqrt{3}+2\left|\sqrt{3}-\sqrt{5}\right|$

$=0,\mathrm{2.10.}\sqrt{3}+2\left(\sqrt{5}-\sqrt{3}\right)$

$=2\sqrt{3}+2\sqrt{5}-2\sqrt{3}=2\sqrt{5}$

(12√12−32√2+45√200):18

=(12√24−32√2+8√2):18

=(14√2−23√2+8√2):18

1212−322+45200):18=(1224−322+82):18=(142−232+82):18=2742.8=542

d) $2\sqrt{{\left(\sqrt{2}-3\right)}^2}+\sqrt{2.{\left(-3\right)}^2}-5\sqrt{{\left(-1\right)}^4}$

$=2\left(3-\sqrt{2}\right)+3\sqrt{2}-5$

$=6-2\sqrt{2}+3\sqrt{2}-5$

$=1+\sqrt{2}$

Answer 30