a)
Ta có :
\(\sqrt{\left(-8^2\right)}\) = \(\sqrt{64}\) = 8 vì 8 > 0 và 82 = 64
b)
Ta có :
\(\sqrt{16}\) = 4 vì 4 > 0 và 42 = 16
c)
Ta có :
\(\sqrt{1,44}\) = 1,2 vì 1,2 > 0 và ( 1,2 )2 = 1,44
có ai giúp tui
\(\left(\sqrt{6}+\sqrt{2}\right)\left(\sqrt{3}-2\right)\sqrt{3}+2\)
\(\frac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\frac{\sqrt{5}+\sqrt{27}}{\sqrt{30}+\sqrt{162}}\)
\(2\sqrt{5}-\sqrt{125}-\sqrt{80}+\sqrt{605}\)
\(\sqrt{8\sqrt{3}-2\sqrt{25\sqrt{12}}+8\sqrt{\sqrt{192}}}\)
2. cho A=\(\sqrt{15a^2-8a\sqrt{15}+16}\)
a. Rút gọn A
b. Tính A khi a=\(\sqrt{\frac{3}{5}}+\sqrt{\frac{5}{3}}\)
1 Tính
\(\sqrt{20,8^2-19,2^2}\)
2 Thực hiện phép tính
a) \(2\sqrt{2}.\left(\sqrt{2}-1\right)+\left(1+\sqrt{2}\right)-2\sqrt{6}\)
b) \(\sqrt{2-\sqrt{2}}.\sqrt{2+\sqrt{2}}+8\)
c) \(\left(\sqrt{2-\sqrt{5}}+\sqrt{3+\sqrt{5}}\right)^2\)
Bài 1 : Cho 3 số dương a,b,c thỏa mãn : \(b\ne c;\sqrt{a}+\sqrt{b}\ne\sqrt{c}\) và \(a+b=\left(\sqrt{a}+\sqrt{b}-\sqrt{c}\right)^2\)
CMR : \(\frac{a+\left(\sqrt{a}-\sqrt{c}\right)^2}{b+\left(\sqrt{b}-\sqrt{c}\right)^2}=\frac{\sqrt{a}-\sqrt{c}}{\sqrt{b}-\sqrt{c}}\)
Thực hiện phép tính
a, \(\frac{10+2\sqrt{10}}{\sqrt{5}+\sqrt{2}}+\frac{8}{1-\sqrt{5}}\)
b. \(\frac{\sqrt{3-\sqrt{5}.\left(3+\sqrt{5}\right)}}{\sqrt{10}+\sqrt{2}}\)
c, \(\frac{1}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{1}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
d, \(\frac{\left(\sqrt{5}+2\right)^2-8\sqrt{5}}{2\sqrt{5}-4}\)
1 Rút gọn
a \(\frac{\sqrt{10}+\sqrt{15}}{\sqrt{6}+\sqrt{12}}\)
b \(\frac{x+\sqrt{xy}}{y+\sqrt{xy}}\)
c \(\sqrt{a^2.\left(a-2\right)^2}\)
2 Tìm x
a \(\sqrt{19x}=15\)
b \(\sqrt{4x^2}=8\)
c) \(\sqrt{4\left(x+1\right)}=\sqrt{8}\)
d \(\sqrt{9\left(2-3x\right)^2}=6\)
Rút gọn biểu thức
a)\(\frac{a-1}{\sqrt[3]{a^2}+\sqrt[3]{a}+1}\)\
b)\(\left(12\sqrt[3]{2}+\sqrt[3]{16}-2\sqrt[3]{2}\right)\left(5\sqrt[3]{4}-3\sqrt[3]{\frac{1}{2}}\right)\)
giải pt a. \(9x+7=6\sqrt{8x+1}+4\sqrt{x+3}\)
b. \(\sqrt{\left(3x-3\right)\left(x+3\right)+16}+\sqrt{5\left(x-2\right)\left(x+4\right)+54}=-x^2+2x+4\)
rút gọn
P=\(\left(\frac{3\sqrt{a}}{\sqrt{a}+4}+\frac{\sqrt{a}}{\sqrt{a}-4}+\frac{4\left(a+2\right)}{16-a}\right):\left(1-\frac{2\sqrt{a}+5}{\sqrt{a}+4}\right)\)
Tính
A=\(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\cdot\sqrt{4-\sqrt{15}}\)
B=\(\left(3-\sqrt{5}\right)\cdot\sqrt{3+\sqrt{5}}+\left(3+\sqrt{5}\right)\cdot\sqrt{3-\sqrt{5}}\)
C=\(\sqrt{2+\sqrt{3}}\cdot\sqrt{2+\sqrt{2+\sqrt{3}}}\cdot\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}\cdot\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{ }}3}}\)
D=\(\sqrt{4+\sqrt{15}}+\sqrt{4-\sqrt{15}}-2\sqrt{3-\sqrt{5}}\)
E=\(\frac{\sqrt{15-10\sqrt{2}}+\sqrt{13+4\sqrt{5}}-\sqrt{11+2\sqrt{10}}}{2\sqrt{3+2\sqrt{2}}+\sqrt{9-4\sqrt{2}}+\sqrt{12+8\sqrt{2}}}\)