Question

$\sqrt[\mathbf{4}]{\mathbf{(17 + 12}\sqrt{\mathbf{2}}\mathbf{)}}\mathbf{=}$

• A. $\sqrt{2} + 1$
• B. $2^{1/4}(\sqrt{2} + 1)$
• C. $2\sqrt{2} + 1$
• D. None

Answer 1

Answer: (A)

$\sqrt{2} + 1$

Answer 2

$\sqrt{(17 + 12\sqrt{2})} = \sqrt{\lbrack 3^{2} + (2\sqrt{2})^{2} + 2.3.2\sqrt{2}\rbrack} = 3 + 2\sqrt{2}$

$\therefore\sqrt[4]{(17 + 12\sqrt{2})} = \sqrt{(3 + 2\sqrt{2})} = \sqrt{2} + 1$ .