Ét o ét giải giúp mình bài 2=)))

Đáp án:

a) $\sqrt{72}-4\sqrt{18}+2\sqrt{32}-\sqrt{50}=-3\sqrt{2}$

b) $\sqrt{(4+\sqrt{5})^2}+\sqrt{(3-\sqrt{5})^2}=7$

c) $\dfrac{1}{\sqrt{7}+2}-\dfrac{1}{\sqrt{7}-2}=-\dfrac{4}{3}$

d) $\sqrt{6-2\sqrt{5}}-\sqrt{14+6\sqrt{5}}=-4$

e) $\dfrac{\sqrt{15}+\sqrt{3}}{\sqrt{5}+1}-6\sqrt{\dfrac{1}{3}}+2\sqrt{27}=5\sqrt{3}$

Giải thích các bước giải:

a)

$\sqrt{72}-4\sqrt{18}+2\sqrt{32}-\sqrt{50}\\=\sqrt{6^2.2}-4\sqrt{3^2.2}+2\sqrt{4^2.2}-\sqrt{5^2.2}\\=6\sqrt{2}-12\sqrt{2}+8\sqrt{2}-5\sqrt{2}\\=-3\sqrt{2}$

b)

$\sqrt{(4+\sqrt{5})^2}+\sqrt{(3-\sqrt{5})^2}\\=4+\sqrt{5}+|3-\sqrt{5}|\\=4+\sqrt{5}+3-\sqrt{5}\\=7$

c)

$\dfrac{1}{\sqrt{7}+2}-\dfrac{1}{\sqrt{7}-2}\\=\dfrac{\sqrt{7}-2-\sqrt{7}-2}{(\sqrt{7}+2)(\sqrt{7}-2)}\\=\dfrac{-4}{7-4}\\=-\dfrac{4}{3}$

d)

$\sqrt{6-2\sqrt{5}}-\sqrt{14+6\sqrt{5}}\\=\sqrt{(\sqrt{5}-1)^2}-\sqrt{(3+\sqrt{5})^2}\\=|\sqrt{5}-1|-(3+\sqrt{5})\\=\sqrt{5}-1-3-\sqrt{5}\\=-4$

e)

$\dfrac{\sqrt{15}+\sqrt{3}}{\sqrt{5}+1}-6\sqrt{\dfrac{1}{3}}+2\sqrt{27}\\=\dfrac{\sqrt{3}(\sqrt{5}+1)}{\sqrt{5}+1}-6.\dfrac{1}{\sqrt{3}}+2\sqrt{3^2.3}\\=\sqrt{3}-2\sqrt{3}+6\sqrt{3}\\=5\sqrt{3}$