Simplification in maths

Square root and Cube root based Simplification questions in maths –

Q64. \sqrt{\left(a^{\smash{-1}}\right)b} × \sqrt{\left(b^{\smash{-1}}\right)c} × \sqrt{\left(c^{\smash{-1}}\right)a} = ?

Ans. 1

Q65. 5\sqrt{3} + \sqrt{75} = 17.32 है तो 14\sqrt{3} + \sqrt{108} = ?

Ans. 34.64

Q66. \sqrt{2+\sqrt{3}} + \sqrt{2-\sqrt{3}}   = ?

Ans. \sqrt{6}

Q67. \cfrac{1}{4-\sqrt{15}} - \cfrac{1}{\sqrt{15}-\sqrt{14}} + \cfrac{1}{\sqrt{14}-\sqrt{13}} - \cfrac{1}{\sqrt{13}-\sqrt{12}} + \cfrac{1}{\sqrt{12}-\sqrt{11}} - \cfrac{1}{\sqrt{11}-\sqrt{10}} + \cfrac{1}{\sqrt{10}-3} - \cfrac{1}{3-\sqrt{8}}

Ans. 4 - 2\sqrt{2}