The value of (√(√12-√8)(√3+√2))/(5+√24) is

Question

The value of \(\sqrt{\frac{(\sqrt{12}-\sqrt8)(\sqrt3+\sqrt2)}{5+\sqrt{24}}}\) is

(a) \(\sqrt6-\sqrt2\)

(b) \(\sqrt6+\sqrt2\)

(c) \(\sqrt6-2\)

(d) \(2-\sqrt6\)

Answer 1

(c) \(\sqrt6-2\)

\(\sqrt{\frac{(\sqrt{12}-\sqrt8)(\sqrt3+\sqrt2)}{5+\sqrt{24}}}\)

= \(\sqrt{(\sqrt6-2)^2} = \sqrt6-2\)