Rút gọn:
2) \(\sqrt{98}-\sqrt{72}+0,5\sqrt{8}\)
3) \(\sqrt{9a}-\sqrt{16a}+\sqrt{49a}\) với a \(\ge\) 0
4) \(\sqrt{16b}+2\sqrt{40b}-3\sqrt{90b}\) với b \(\ge\) 0
Rút gọn các biểu thức :
a) \(\sqrt{75}+\sqrt{48}-\sqrt{300}\)
b) \(\sqrt{98}-\sqrt{72}+0,5\sqrt{8}\)
c) \(\sqrt{9a}-\sqrt{16a}+\sqrt{49a}\) với \(a\ge0\)
d) \(\sqrt{16b}+2\sqrt{40b}-3\sqrt{90b}\) với \(b\ge0\)
ĐS: a) 3√5;35;
b) 9√22;922;
c) 15√2−√5;152−5;
d) 17√25.
a) \(\sqrt{75}+\sqrt{48}-\sqrt{300}\) = \(5\sqrt{3}+4\sqrt{3}-10\sqrt{3}\) = \(-\sqrt{3}\)
b) \(\sqrt{98}-\sqrt{72}+0,5\sqrt{8}\) = \(7\sqrt{2}-6\sqrt{2}+\sqrt{2}\) = \(2\sqrt{2}\)
c) \(\sqrt{9a}-\sqrt{16a}+\sqrt{49a}\) = \(3\sqrt{a}-4\sqrt{a}+7\sqrt{a}\) = \(6\sqrt{a}\)
d) \(\sqrt{16b}+2\sqrt{40b}-3\sqrt{90b}\) = \(4\sqrt{b}+4\sqrt{10b}-9\sqrt{10b}\)
= \(4\sqrt{b}-5\sqrt{10b}\)
Rút gọn: (Giải chi tiết từng bước)
4) \(\sqrt{16b}+2\sqrt{40b}-3\sqrt{90b}\) với b \(\ge\) 0
4) \(\sqrt{16b}+2\sqrt{40b}-3\sqrt{90b}\)
\(=\sqrt{4^2\cdot b}+2\sqrt{2^2\cdot10b}-3\sqrt{3^2\cdot10b}\)
\(=4\sqrt{b}+2\cdot2\sqrt{10b}-3\cdot3\sqrt{10b}\)
\(=4\sqrt{b}+4\sqrt{10b}-9\sqrt{10b}\)
\(=4\sqrt{b}+\left(4\sqrt{10b}-9\sqrt{10b}\right)\)
\(=4\sqrt{b}-5\sqrt{10b}\)
`a, sqrt(16b) + 2 sqrt(40b) - 3 sqrt(90b)`
`= 4sqrtb + 2sqrt(8.5b) - 3 sqrt(9.10b)`
`= 4 sqrt b + 4sqrt(10b) - 9 sqrt(10b)`
`= 4sqrtb-5sqrt(10b)`.
Bài 7: Rút Gọn Các Biểu Thức Sau
a. 5\(\sqrt{25^2}\) - 25x Với X<O
B \(\sqrt{49a^2}\) + 3a Với a \(\ge\) 0
C \(\sqrt{16a^4}\) + 6a\(^2\) Với a Bất Kì
d 3\(\sqrt{9a^6}\) - 6a\(^3\) với a bất kì
e 3\(\sqrt{9a^6}\) - 6a\(^3\) Với a\(\ge\) 0
f \(\sqrt{16a^{10}}\) + 6a\(^5\) với a \(\le0\)
b: B=căn 49a^2+3a
=|7a|+3a
=7a+3a(a>=0)
=10a
c: C=căn16a^4+6a^2
=4a^2+6a^2
=10a^2
d: \(D=3\cdot3\cdot\sqrt{a^6}-6a^3=6\cdot\left|a^3\right|-6a^3\)
TH1: a>=0
D=6a^3-6a^3=0
TH2: a<0
D=-6a^3-6a^3=-12a^3
e: \(E=3\sqrt{9a^6}-6a^3\)
\(=3\cdot\sqrt{\left(3a^3\right)^2}-6a^3\)
=3*3a^3-6a^3(a>=0)
=3a^3
f: \(F=\sqrt{16a^{10}}+6a^5\)
\(=\sqrt{\left(4a^5\right)^2}+6a^5\)
=-4a^5+6a^5(a<=0)
=2a^5
Rút gọn biểu thức \(\sqrt{16b}\) + \(2\sqrt{40b}\) - \(3\sqrt{90b}\) với b ≥ 0 là
\(\sqrt{16b}+2\sqrt{40b}-3\sqrt{90b}=4\sqrt{b}+2.2\sqrt{10b}-3.3\sqrt{10b}=4\sqrt{b}+4\sqrt{10b}-9\sqrt{10b}=4\sqrt{b}-5\sqrt{10b}\)
giai pt:
\(\sqrt{16b}+2\sqrt{40b}-30\sqrt{90b}\) voi b\(\ge\)0
\(\sqrt{16b}+2\sqrt{40b}-30\sqrt{90b}\)
\(=\sqrt{16}\sqrt{b}+2\sqrt{40}\sqrt{b}-30\sqrt{90}\sqrt{b}\)
\(=\sqrt{b}\left(\sqrt{16}+2\sqrt{40}-30\sqrt{90}\right)\)
\(=\sqrt{b}\left(4+4\sqrt{10}-90\sqrt{10}\right)\)
\(=\sqrt{b}\left(4-86\sqrt{10}\right)\)
1) thực hiện phép tính và rút gọn biểu thức
a) A=\(\sqrt{9a}-\sqrt{16a}-\sqrt{49a}\) với \(a\ge0\)
b) B=\(\dfrac{3+2\sqrt{3}}{\sqrt{3}}+\dfrac{2+\sqrt{2}}{\sqrt{2}}-\left(\sqrt{3}+\sqrt{2}\right)\)
lm nhanh giúp mk nhé mk đang cần gấp
a) \(A=\sqrt{9a}-\sqrt{16a}-\sqrt{49a}=3\sqrt{a}-4\sqrt{a}-7\sqrt{a}=-8\sqrt{a}\)
b) \(B=\dfrac{3+2\sqrt{3}}{\sqrt{3}}+\dfrac{2+\sqrt{2}}{\sqrt{2}}-\left(\sqrt{3}+\sqrt{2}\right)\)
\(=\dfrac{\sqrt{3}\left(2+\sqrt{3}\right)}{\sqrt{3}}+\dfrac{\sqrt{2}\left(\sqrt{2}+1\right)}{\sqrt{2}}-\left(\sqrt{3}+\sqrt{2}\right)\)
\(=2+\sqrt{3}+\sqrt{2}+1-\sqrt{3}-\sqrt{2}=3\)
Rút gọn: \(\sqrt{16b}+2\sqrt{40b}-3\sqrt{90b}\)
\(\sqrt{16b}+2\sqrt{40b}-3\sqrt{90b}\) với b lớn hơn hoặc bằng 0
\(\sqrt{16b}+2\sqrt{40b}-3\sqrt{90b}\)
\(=\sqrt{16}\sqrt{b}+2\sqrt{40}\sqrt{b}-3\sqrt{90}\sqrt{b}\)
\(=\sqrt{b}\left(\sqrt{16}+2\sqrt{40}-3\sqrt{90}\right)\)
\(=\sqrt{b}\left(4+4\sqrt{10}-9\sqrt{10}\right)\)
\(=\sqrt{b}\left(4-5\sqrt{10}\right)\)
1) \(\sqrt{9a^2.b^2}\) với a<0, b<0
2) \(\sqrt{3a}.\sqrt{27a}\) với a \(\ge\)0
3) \(\sqrt{3a^5}.12a\) với a>0
4) \(\sqrt{5a}.\sqrt{45a}-3a\) ( với a ≥ 0)
5) \(\sqrt{3+\sqrt{a}}\).\(\sqrt{3-\sqrt{a}}\)
6) \(\sqrt{3+\sqrt{5}}\). \(\sqrt{3\sqrt{5}}\)
\(1) \sqrt{9a^2.b^2}\)=3ab
\(2) \sqrt{3a}.\sqrt{27a}=\sqrt{3a}.3\sqrt{3a}=9a\)
\(3) \sqrt{3a^5}.12a=12\sqrt{3a^7}\)
\(4) \sqrt{5a}.\sqrt{45a}-3a=15a-3a=12a\)
\(5) \sqrt{3+\sqrt{a}}.\sqrt{3-\sqrt{a}}=\sqrt{(3+\sqrt{a}).(3-\sqrt{a})} =\sqrt{9-a} \)
\(6) \sqrt{3+\sqrt{5}}.\sqrt{3\sqrt{5}} =\sqrt{\sqrt{3\sqrt{5}}.(3+\sqrt{5})} =\sqrt{9+\sqrt{15}}\)
1) \(\sqrt{9a^2b^2}=3ab\)
2) \(\sqrt{3a}\cdot\sqrt{27a}=9a\)
4) \(\sqrt{5a}\cdot\sqrt{45a}-3a=15a-3a=12a\)