JIPMAT 2023 (QA) - 3+sqrt(5)= | PYQs + Solutions

JIPMAT 2023

Algebra

Indices

Easy

$\sqrt{3+\sqrt{5}}=$

\sqrt{2}+1

\sqrt{\frac{5}{2}}+\sqrt{\frac{1}{2}}

\sqrt{\frac{7}{2}}-\sqrt{\frac{1}{2}}

\sqrt{\frac{9}{2}}-\sqrt{\frac{3}{2}}

Correct Option: 2

To solve this easily, we can go through the options and square the given options to see if they equate

3+\sqrt5

Look at the second option.

We know that

(a+b)^2=a^2+b^2+2ab

Squaring the second option, we'll get:

\frac{5}{2}+\frac{1}{2}+2(\sqrt{\frac{5}{2}})(\sqrt{\frac{1}{2}})

\frac{6}{2}+\frac{2\sqrt5}{2}=3+\sqrt5