Question

tính giá trị của biểu thức:
a) \(\sqrt{75}+\sqrt{48}-\sqrt{300}\)

b) \(\sqrt{81a}-\sqrt{36a}+\sqrt{144a}\left(a\ge0\right)\)

c) \(\dfrac{4}{\sqrt{5}-2}-\dfrac{4}{\sqrt{5}+2}\)

d) \(\dfrac{a\sqrt{b}-b\sqrt{b}}{\sqrt{a}-\sqrt{b}}\left(a\ge0;b\ge0;a\ne b\right)\)

Answer 1

a, \(\sqrt{75}+\sqrt{48}-\sqrt{300}\)

\(=5\sqrt{3}+4\sqrt{3}-10\sqrt{3}\)

\(=-\sqrt{3}\)

b, \(\sqrt{81a}-\sqrt{36a}+\sqrt{144a}\)

\(=9\sqrt{a}-6\sqrt{a}+12\sqrt{a}\)

\(=15\sqrt{a}\)

c, \(\dfrac{4}{\sqrt{5}-2}-\dfrac{4}{\sqrt{5}+2}\)

\(=\dfrac{4\sqrt{5}+8-4\sqrt{5}+8}{\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)}\)

\(=\dfrac{16}{5-4}=16\)

d, \(\dfrac{a\sqrt{b}-b\sqrt{a}}{\sqrt{a}-\sqrt{b}}=\dfrac{\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)}{\sqrt{a}-\sqrt{b}}=\sqrt{ab}\)