\(\sqrt{6-2\sqrt{5}}=\sqrt{5-2\sqrt{5}+1}=\sqrt{\left(\sqrt{5}-1\right)^2}=\sqrt{5}-1\)
\(\sqrt{6-2\sqrt{5}}=1+5-2\sqrt{5}=1-2\sqrt{5}+5=\left(1-\sqrt{5}\right)^2=\sqrt{5}-1\)
* Tính giá trị của biểu thức:
a. A=\(2\sqrt{2}-3\sqrt{18}+4\sqrt{32}-\sqrt{50}\)
b. B=\(\sqrt{\left(1-\sqrt{5}\right)^2}+\sqrt{6+2\sqrt{5}}\)
c. C=\(\dfrac{1}{2-\sqrt{6}}+\dfrac{1}{2+\sqrt{6}}\)
Tính:
\(\left(\dfrac{6-2\sqrt{2}}{3-\sqrt{2}}-\dfrac{5}{\sqrt{5}}\right):\dfrac{1}{2+\sqrt{5}}\)
Tính a=\(\dfrac{\sqrt[3]{10+6\sqrt{3}}.\left(\sqrt{3}-1\right)}{\sqrt{6+2\sqrt{5}}-5}\)
b, a= \(\sqrt[3]{2-\sqrt{3}}+\sqrt[3]{2+\sqrt{3}}\) CMR \(\dfrac{64}{\left(a^2-3\right)^3}-3a\) ∈ Z
Tính: ( Nhân cả tử lẫn mẫu với biểu thức liên hợp )
\(\dfrac{\sqrt{3}}{\sqrt{\sqrt{6}+}-1}-\dfrac{\sqrt{3}}{\sqrt{\sqrt{6}+1}+1}\)
\(\dfrac{2\sqrt{3}}{\sqrt{2}+\sqrt{3}+\sqrt{5}}+\dfrac{2}{\sqrt{6}+\sqrt{10}}\)
Tính:
\(A=\sqrt{27}-2\sqrt{48}+3\sqrt{75}\)
\(B=\sqrt{\left(\sqrt{5}-2\right)^2}-\sqrt{\left(\sqrt{5}-3\right)^2}\)
\(C=\sqrt{\left(2\sqrt{3}+1\right)^2}+\sqrt{\left(2\sqrt{3}-5\right)^2}\)
\(D=\sqrt{9-4\sqrt{5}}-\sqrt{14+6\sqrt{5}}\)
\(E=\dfrac{4}{\sqrt{5}-2}-\dfrac{32}{\sqrt{5}+1}\)
\(M=\dfrac{10}{3\sqrt{2}-4}+\dfrac{28}{3\sqrt{2}+2}\)
please help ;-;
Tính:
\(A=3\sqrt{20}-\sqrt{45}+2\sqrt{18}+\sqrt{72}\)
\(B=\dfrac{12}{3-\sqrt{5}}-\dfrac{16}{\sqrt{5}+1}\)
\(C=10\sqrt{\dfrac{1}{5}}+\dfrac{1}{5}\sqrt{125}-2\sqrt{20}\)
\(E=\sqrt{\left(\sqrt{3}+1\right)^2}-\sqrt{\left(\sqrt{3}-2\right)^2}\)
\(F=\sqrt{6+2\sqrt{5}}-\sqrt{9-4\sqrt{5}}\)
Tính:
\(A=3\sqrt{20}-\sqrt{45}+2\sqrt{18}+\sqrt{72}\)
\(B=\dfrac{12}{3-\sqrt{5}}-\dfrac{16}{\sqrt{5}+1}\)
\(C=10\sqrt{\dfrac{1}{5}}+\dfrac{1}{5}\sqrt{125}-2\sqrt{20}\)
\(E=\sqrt{\left(\sqrt{3}+1\right)^2}-\sqrt{\left(\sqrt{3}-2\right)^2}\)
\(F=\sqrt{6+2\sqrt{5}}-\sqrt{9-4\sqrt{5}}\)
Bài 1: Cho biểu thức A = 1 - \(\dfrac{\sqrt{x}}{1+\sqrt{x}}\), B = \(\dfrac{\sqrt{x}-1}{\sqrt{x}-2}\)+ \(\dfrac{\sqrt{x}+2}{3-\sqrt{x}}\)- \(\dfrac{10-5\sqrt{x}}{x-5\sqrt{x}+6}\)
(với x ≥ 0, x ≠ 4, x ≠ 9)
a, Tính giá trị của A biết x = 6-2\(\sqrt{5}\)
b, Rút gọn P = A : B
c, Tìm giá trị nhỏ nhất của P
Tính:
\(A=2\sqrt{\left(-3\right)^6}+2\sqrt{\left(-2\right)^4}-4\sqrt{\left(-2\right)^6}\)
\(B=\sqrt{\left(\sqrt{2}-2\right)^2}+\sqrt{\left(\sqrt{2}-3\right)^2}\)
\(C=\sqrt{\left(3-\sqrt{3}\right)^2}-\sqrt{\left(1+\sqrt{3}\right)^2}\)
\(D=\sqrt{\left(5+\sqrt{6}\right)^2}-\sqrt{\left(\sqrt{6}-5\right)^2}\)
\(E=\sqrt{17^2-8^2}-\sqrt{3^2+4^2}\)
Tính
\(\left(\sqrt{2}+1\right)\left(\sqrt{3}+1\right)\left(\sqrt{6}+1\right)\left(5-2\sqrt{2}-\sqrt{3}\right)\)
