Question

1)\(\sqrt{9a}\) - \(\sqrt{16a}\) +\(\sqrt{49a}\) (a \(\ge\) 0)

2)2\(\sqrt{40\sqrt{12}}\) - 2\(\sqrt{\sqrt{75}}\) - 3\(\sqrt{5\sqrt{80}}\)

3)\(\dfrac{\sqrt{X^3}-1}{\sqrt{X}-1}\)

Answer 1

1) \(\sqrt{9a}-\sqrt{16a}+\sqrt{49a}\left(a\ge0\right)\)\(=3\sqrt{a}-4\sqrt{a}+7\sqrt{a}\) \(=6\sqrt{a}\)

2) \(2\sqrt{40\sqrt{12}}-2\sqrt{\sqrt{75}}-3\sqrt{5\sqrt{80}}\)

= \(2\sqrt{80\sqrt{3}}-2\sqrt{5\sqrt{3}}-3\sqrt{20\sqrt{5}}\)

= \(8\sqrt{5\sqrt{3}}-2\sqrt{5\sqrt{3}}-6\sqrt{5\sqrt{5}}\)

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

3) \(\dfrac{\sqrt{x^3}-1}{\sqrt{x}-1}\) = \(\dfrac{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}{\sqrt{x}-1}\) = \(x+\sqrt{x}+1\)