MBApyq

Simplification of Surds

CMAT 2026 · Quantitative Techniques & Data Interpretation · Medium · Algebra

All CMAT 2026 questionsMore Algebra questionsAll CMAT QTDI

The value of expression 5+2+5−25+1\frac{\sqrt{\sqrt{5}+2} + \sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}} is

  1. A.

    1

  2. B.

    \sqrt{2}

  3. C.

    4

  4. D.

    \sqrt{5}

Answer

B

Explanation

Let numerator N=5+2+5−2N = \sqrt{\sqrt{5}+2} + \sqrt{\sqrt{5}-2}. N2=(5+2)+(5−2)+2(5)2−4=25+2=2(5+1)N^2 = (\sqrt{5}+2) + (\sqrt{5}-2) + 2\sqrt{(\sqrt{5})^2 - 4} = 2\sqrt{5} + 2 = 2(\sqrt{5}+1). N=25+1N = \sqrt{2}\sqrt{\sqrt{5}+1}. Thus, N5+1=2\frac{N}{\sqrt{\sqrt{5}+1}} = \sqrt{2}.

Related Algebra questions

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace