\(\dfrac{1}{3}\sqrt{18}+2\sqrt{45}-\sqrt{72}+3\sqrt{20}\)

\(=\dfrac{1}{3}\sqrt{9\times2}+2\sqrt{9\times5}-\sqrt{9\times8}+3\sqrt{4\times5}\)

\(=\sqrt{2}+6\sqrt{5}-6\sqrt{2}+6\sqrt{5}\) \(=12\sqrt{5}-5\sqrt{2}\)

\(\dfrac{1}{3}\sqrt{18}+2\sqrt{45}-\sqrt{72}+3\sqrt{20}\)

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

\(=12\sqrt{5}-5\sqrt{2}\)

a: \(=\sqrt{5\cdot7\cdot11\cdot11\cdot35}=\sqrt{35^2\cdot11^2}=35\cdot11=385\)

b: \(=\sqrt{169-144}=\sqrt{25}=5\)

c: \(=2\sqrt{5}-3\sqrt{5}+5\cdot3\sqrt{2}+6\sqrt{2}\)

\(=-\sqrt{5}+21\sqrt{2}\)

√20-√45+3√18+√72

=2√5-3√5+9√2+6√2

=-√5+15√2

\(\sqrt{20}-\sqrt{45}+3\sqrt{18}+\sqrt{72}\)

\(=\sqrt{4.5}-\sqrt{9.5}+3\sqrt{18}+\sqrt{4.18}\)

\(=2\sqrt{5}-3\sqrt{5}+3\sqrt{18}+2\sqrt{18}\)

\(=-\sqrt{5}+5\sqrt{18}\)

\(\sqrt{20}-\sqrt{45}+3\sqrt{18}+\sqrt{72}\)

\(=2\sqrt{5}-3\sqrt{5}+3\sqrt{18}+2\sqrt{18}\)

\(=-\sqrt{5}+5\sqrt{18}\)

0201

a) Ta có: \(A=3\sqrt{20}-\sqrt{45}+2\sqrt{18}+\sqrt{72}\)

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

\(=3\sqrt{5}+12\sqrt{2}\)

b) Ta có: \(B=\dfrac{12}{3-\sqrt{5}}-\dfrac{16}{\sqrt{5}+1}\)

\(=\dfrac{12\left(3+\sqrt{5}\right)}{4}-\dfrac{16\left(\sqrt{5}-1\right)}{4}\)

\(=3\left(3+\sqrt{5}\right)-4\left(\sqrt{5}-1\right)\)

\(=9+3\sqrt{5}-4\sqrt{5}+4\)

\(=13-\sqrt{5}\)

c) Ta có: \(C=10\sqrt{\dfrac{1}{5}}+\dfrac{1}{5}\sqrt{125}-2\sqrt{20}\)

\(=\dfrac{10}{\sqrt{5}}+\dfrac{1}{5}\cdot5\sqrt{5}-2\cdot2\sqrt{5}\)

\(=2\sqrt{5}+\sqrt{5}-4\sqrt{5}\)

\(=-\sqrt{5}\)

e) Ta có: \(E=\sqrt{\left(\sqrt{3}+1\right)^2}-\sqrt{\left(\sqrt{3}-2\right)^2}\)

\(=\sqrt{3}+1-2+\sqrt{3}\)

\(=2\sqrt{3}-1\)

f) Ta có: \(F=\sqrt{6+2\sqrt{5}}-\sqrt{9-4\sqrt{5}}\)

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

=3

e) Ta có: \(E=\sqrt{\left(\sqrt{3}+1\right)^2}-\sqrt{\left(\sqrt{3}-2\right)^2}\)

\(=\sqrt{3}+1-2+\sqrt{3}\)

\(=2\sqrt{3}-1\)

f) Ta có: \(F=\sqrt{6+2\sqrt{5}}-\sqrt{9-4\sqrt{5}}\)

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

=3

a) Ta có: \(A=3\sqrt{20}-\sqrt{45}+2\sqrt{18}+\sqrt{72}\)

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

\(=3\sqrt{5}+12\sqrt{2}\)

b) Ta có: \(B=\dfrac{12}{3-\sqrt{5}}-\dfrac{16}{\sqrt{5}+1}\)

\(=\dfrac{12\left(3+\sqrt{5}\right)}{4}-\dfrac{16\left(\sqrt{5}-1\right)}{4}\)

\(=3\left(3+\sqrt{5}\right)-4\left(\sqrt{5}-1\right)\)

\(=9+3\sqrt{5}-4\sqrt{5}+4\)

\(=13-\sqrt{5}\)

\(A=2\sqrt{5}-\sqrt{45}+2\sqrt{20}=2\sqrt{5}-\sqrt{3^2.5}+2\sqrt{2^2.5}=2\sqrt{5}-3\sqrt{5}+4\sqrt{5}=3\sqrt{5}\)

\(B=\left(\sqrt{18}-\frac{1}{2}\cdot\sqrt{32}+12\sqrt{2}\right):\sqrt{2}=\left(3\sqrt{2}-\frac{1}{2}\cdot4\sqrt{2}+12\sqrt{2}\right):\sqrt{2}\)

\(=13\sqrt{2}:\sqrt{2}=13\)

\(C=\left(\sqrt{12}+2\sqrt{27}-3\sqrt{3}\right)\cdot\sqrt{3}=\left(2\sqrt{3}+6\sqrt{3}-3\sqrt{3}\right)\cdot\sqrt{3}=5\sqrt{3}\cdot\sqrt{3}=15\)

\(D=\sqrt{20}-\sqrt{45}+3\sqrt{18}+\sqrt{72}=2\sqrt{5}-3\sqrt{5}+9\sqrt{2}+6\sqrt{2}=-\sqrt{5}+15\sqrt{2}\)