Bài 1:
a.
\(\sqrt{18}-2\sqrt{50}+3\sqrt{8}=\sqrt{3^2.2}-2\sqrt{5^2.2}+3\sqrt{2^2.2}\)
\(=3\sqrt{2}-10\sqrt{2}+6\sqrt{2}=(3-10+6)\sqrt{2}=-\sqrt{2}\)
b.
\(B=\sqrt{3^2.3}-2\sqrt{3^2.\frac{1}{3}}+\frac{\sqrt{3}(1-\sqrt{3})}{\sqrt{3}}\)
\(=3\sqrt{3}-2\sqrt{3}+1-\sqrt{3}=1\)
c.
\(C=\frac{5(\sqrt{7}-\sqrt{2})}{(\sqrt{7}-\sqrt{2})(\sqrt{7}+\sqrt{2})}-\sqrt{(\sqrt{7}-1)^2}+\sqrt{2}\)
\(=\frac{5(\sqrt{7}-\sqrt{2})}{7-2}-|\sqrt{7}-1|+\sqrt{2}=\sqrt{7}-\sqrt{2}-\sqrt{7}+1+\sqrt{2}=1\)
Bài 2:
a.
\(=\frac{1}{2}\sqrt{4^2.3}-2\sqrt{5^2.3}-\frac{\sqrt{11}.\sqrt{3}}{\sqrt{11}}+5\sqrt{\frac{4}{3}}\)
\(=\frac{1}{2}.4\sqrt{3}-2.5\sqrt{3}-\sqrt{3}+\frac{10}{\sqrt{3}}\)
\(=2\sqrt{3}-10\sqrt{3}-\sqrt{3}+\frac{10\sqrt{3}}{3}=\frac{-17\sqrt{3}}{3}\)
b.
\(=\sqrt{(\sqrt{5}+1)^2}-\sqrt{(\sqrt{5}-1)^2}-\sqrt[3]{2^3}\)
\(=|\sqrt{5}+1|-|\sqrt{5}-1|-2=\sqrt{5}+1-(\sqrt{5}-1)-2=0\)
c. ĐK: $a>0$
\(=5\sqrt{2a}-\sqrt{5^2.2a}-2\sqrt{a^2.a}+4\sqrt{4^2.2a}\)
\(=5\sqrt{2a}-5\sqrt{2a}-2a\sqrt{a}+16\sqrt{2a}=16\sqrt{2a}-2a\sqrt{a}\)
Bài 1:
a) Ta có: \(A=\sqrt{18}-2\sqrt{50}+3\sqrt{8}\)
\(=3\sqrt{2}-2\cdot5\sqrt{2}+3\cdot2\sqrt{2}\)
\(=-\sqrt{2}\)
b) Ta có: \(B=\sqrt{27}-6\sqrt{\dfrac{1}{3}}+\dfrac{\sqrt{3}-3}{\sqrt{3}}\)
\(=3\sqrt{3}-2\sqrt{3}+1-\sqrt{3}\)
=1
Bài 2:
c) Ta có: \(5\sqrt{2a}-\sqrt{50a}-2\sqrt{a^3}+4\sqrt{32a}\)
\(=5\sqrt{2a}-5\sqrt{2a}-2a\sqrt{a}+16\sqrt{2a}\)
\(=16\sqrt{2a}-2a\sqrt{a}\)