a)\(\sqrt{28-16\sqrt{3}}=\sqrt{12-2.4.2\sqrt{3}+16}=\sqrt{\left(2\sqrt{3}\right)^2-2.4.2\sqrt{3}+4^2}=\sqrt{\left(2\sqrt{3}-4\right)^2}\)\(=\left|2\sqrt{3}-4\right|=4-2\sqrt{3}\)

b) \(\sqrt{29-12\sqrt{5}}=\sqrt{3^2-2.3.2\sqrt{5}+\left(2\sqrt{5}\right)^2}=\sqrt{\left(3-2\sqrt{5}\right)^2}=2\sqrt{5}-3\)

c)\(\sqrt{23-\sqrt{240}}=\sqrt{23-4\sqrt{15}}=\sqrt{\left(2\sqrt{5}\right)^2-2.\sqrt{3}.2\sqrt{5}+\left(\sqrt{3}\right)^2}\)

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

d)\(\sqrt{33-12\sqrt{6}}=\sqrt{\left(2\sqrt{6}\right)^2-2.3.2\sqrt{6}+3^2}=\sqrt{\left(2\sqrt{6}-3\right)^2}=2\sqrt{6}-3\)

Trả lời:

a)\(\sqrt{28-16\sqrt{3}}\)

\(=\sqrt{16-16\sqrt{3}+12}\)

\(=\sqrt{\left(4-2\sqrt{3}\right)^2}\)

\(=4-2\sqrt{3}\)

b) \(\sqrt{29-12\sqrt{5}}\)

\(=\sqrt{20-12\sqrt{5}+9}\)

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

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

c) \(\sqrt{23-\sqrt{240}}\)

\(=\sqrt{23-4\sqrt{15}}\)

\(=\sqrt{20-4\sqrt{15}+3}\)

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

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

d) \(\sqrt{33-12\sqrt{6}}\)

\(=\sqrt{24-12\sqrt{6}+9}\)

\(=\sqrt{\left(2\sqrt{6}-3\right)^2}\)

\(=2\sqrt{6}-3\)

a) Ta có: \(A=\sqrt{23+6\sqrt{10}}-\sqrt{23-6\sqrt{10}}\)

\(=\sqrt{18+2\cdot3\sqrt{2}\cdot\sqrt{5}+5}-\sqrt{18-2\cdot3\sqrt{2}\cdot\sqrt{5}+5}\)

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

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

\(=2\sqrt{5}\)

b) Ta có: \(B=\left(\dfrac{2+\sqrt{2}}{\sqrt{2}+1}+1\right)\left(\dfrac{2-\sqrt{2}}{\sqrt{2}-1}-1\right)\)

\(=\left(\dfrac{\sqrt{2}\left(\sqrt{2}+1\right)}{\sqrt{2}+1}+1\right)\left(\dfrac{\sqrt{2}\left(\sqrt{2}-1\right)}{\sqrt{2}-1}-1\right)\)

\(=\left(\sqrt{2}+1\right)\left(\sqrt{2}-1\right)\)

=2-1=2

Anh Quyền à:

Đáp án như sau:

cau a, 47

câu b, 6/35

đúng 100%

tích đi

\(\sqrt{4}\)+x=\(\sqrt{16}\)+\(\sqrt{25}\)

2+x=4+5

2+x=9

x=9-2=7

12+63=6:x

75=6:x

6:x=75

x=6:75=0,08

a) 2 + x = 4 + 5

   2 + x = 9

        x = 9 - 2

        x = 7

b) 12 + 23 = 6 : x

   6 : x = 12 + 23

   6 : x = 35

       x = 6 : 35

       x = 6/35

a)

\((2\sqrt{5}-\sqrt{7})(2\sqrt{5}+\sqrt{7})=(2\sqrt{5})^2-(\sqrt{7})^2=13\)

b)

\((\sqrt{5-2\sqrt{6}}+\sqrt{2})\sqrt{3}=(\sqrt{2+3-2\sqrt{2.3}}+\sqrt{2})\sqrt{3}\)

\(=(\sqrt{(\sqrt{3}-\sqrt{2})^2}+\sqrt{2})\sqrt{3}=(\sqrt{3}-\sqrt{2}+\sqrt{2})\sqrt{3}=\sqrt{3}.\sqrt{3}=3\)

c)

\(\sqrt{7-4\sqrt{3}}+\sqrt{7+4\sqrt{3}}=\sqrt{2^2+3-2.2\sqrt{3}}+\sqrt{2^2+3+2.2\sqrt{3}}\)

\(=\sqrt{(2-\sqrt{3})^2}+\sqrt{(2+\sqrt{3})^2}=2-\sqrt{3}+2+\sqrt{3}=4\)

d)

\(\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}=\sqrt{3^2+6-2.3\sqrt{6}}+\sqrt{9+24-2\sqrt{9.24}}\)

\(=\sqrt{(3-\sqrt{6})^2}+\sqrt{(\sqrt{24}-3)^2}=3-\sqrt{6}+\sqrt{24}-3\)

\(=\sqrt{6}\)

e)

\(\sqrt{3+\sqrt{5}}+\sqrt{3-\sqrt{5}}=\sqrt{\frac{6+2\sqrt{5}}{2}}+\sqrt{\frac{6-2\sqrt{5}}{2}}\)

\(=\sqrt{\frac{5+1+2\sqrt{5.1}}{2}}+\sqrt{\frac{5+1-2\sqrt{5.1}}{2}}=\sqrt{\frac{(\sqrt{5}+1)^2}{2}}+\sqrt{\frac{(\sqrt{5}-1)^2}{2}}\)

\(=\frac{\sqrt{5}+1}{\sqrt{2}}+\frac{\sqrt{5}-1}{\sqrt{2}}=\sqrt{10}\)

g)

\(\sqrt{8-2\sqrt{15}}-\sqrt{23-4\sqrt{15}}=\sqrt{3+5-2\sqrt{3.5}}-\sqrt{20+3-2\sqrt{20.3}}\)

\(=\sqrt{(\sqrt{5}-\sqrt{3})^2}-\sqrt{(\sqrt{20}-\sqrt{3})^2}\)

\(=\sqrt{5}-\sqrt{3}-(\sqrt{20}-\sqrt{3})=\sqrt{5}-\sqrt{20}=-\sqrt{5}\)

\(\sqrt{29+12\sqrt{5}}-\sqrt{29-12\sqrt{5}}=\left(2\sqrt{5}+3\right)-\left(2\sqrt{5}-3\right)=6\)

\(\sqrt{8-2\sqrt{15}}-\sqrt{23-4\sqrt{15}}=\left(\sqrt{5}-\sqrt{3}\right)-\left(2\sqrt{5}-\sqrt{3}\right)=-\sqrt{5}\)

\(\sqrt{8-12\sqrt{5}}+\sqrt{48+6\sqrt{15}}=\left(\sqrt{5}-\sqrt{3}\right)+\left(3\sqrt{5}+\sqrt{3}\right)=4\sqrt{5}\)

\(\sqrt{49-5\sqrt{96}}+\sqrt{49+5\sqrt{96}}=\left(5-2\sqrt{6}\right)+\left(5+2\sqrt{6}\right)=10\)

\(\sqrt{15-6\sqrt{15}}+\sqrt{33-12\sqrt{6}}\) đề này sai ạ

\(\sqrt{16-6\sqrt{7}}+\sqrt{64-24\sqrt{7}}=\left(3-\sqrt{7}\right)+\left(6-2\sqrt{7}\right)=9-3\sqrt{7}\)

\(\sqrt{14-6\sqrt{5}}+\sqrt{14+6\sqrt{5}}=\left(3-\sqrt{5}\right)+\left(3+\sqrt{5}\right)=6\)

\(\sqrt{1-6\sqrt{2}}+\sqrt{11-6\sqrt{2}}\)

\(\sqrt{13+4\sqrt{10}}+\sqrt{13-4\sqrt{10}}=\left(2\sqrt{2}+5\right)+\left(2\sqrt{2}-5\right)=4\sqrt{2}\)

\(\sqrt{46-6\sqrt{5}}+\sqrt{29-12\sqrt{5}}=\left(3\sqrt{5}-1\right)+\left(2\sqrt{5}-3\right)=5\sqrt{5}-4\)

#Học tốt ạ

\(\sqrt{8-2\sqrt{15}}+\sqrt{48+6\sqrt{15}}\\ =\sqrt{5-2\cdot\sqrt{5}\cdot\sqrt{3}+3}+\sqrt{45+2\cdot3\sqrt{5}\cdot\sqrt{3}+3}\\ =\sqrt{\left(\sqrt{5}\right)^2-2\cdot\sqrt{5}\cdot\sqrt{3}+\left(\sqrt{3}\right)^2}+\sqrt{\left(3\sqrt{5}\right)^2+2\cdot3\sqrt{5}\cdot\sqrt{3}+\left(\sqrt{3}\right)^2}\\ =\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}+\sqrt{\left(3\sqrt{5}+\sqrt{3}\right)^2}\\ =\sqrt{5}-\sqrt{3}+3\sqrt{5}+\sqrt{3}=4\sqrt{5}\)

\(\sqrt{8-\sqrt{60}}-\sqrt{23-\sqrt{240}}\\ =\sqrt{8-\sqrt{4\cdot15}}-\sqrt{23-\sqrt{4\cdot60}}\\ =\sqrt{8-2\sqrt{15}}-\sqrt{23-2\sqrt{60}}\\ =\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}-\sqrt{20-2\cdot\sqrt{20}\cdot\sqrt{3}+3}\\ =\sqrt{5}-\sqrt{3}-\sqrt{\left(\sqrt{20}-\sqrt{3}\right)^2}\\ =\sqrt{5}-\sqrt{3}-\sqrt{20}+\sqrt{3}\\ =\sqrt{5}-2\sqrt{5}=-\sqrt{5}\)