sqrt{3 + sqrt{5}} is equal to | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let $\sqrt{3 + \sqrt{5}} = \sqrt{x} + \sqrt{y}$.Squaring both sides,we get $3 + \sqrt{5} = x + y + 2\sqrt{xy}$.Comparing the rational and irration

Vedclass · Accepted Answer

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

Vedclass · Answer

(C) Let $\sqrt{3 + \sqrt{5}} = \sqrt{x} + \sqrt{y}$.Squaring both sides,we get $3 + \sqrt{5} = x + y + 2\sqrt{xy}$.Comparing the rational and irrational parts,we have $x + y = 3$ and $2\sqrt{xy} = \sqrt{5}$,which implies $4xy = 5$,so $xy = \frac{5}{4}$.We know that $(x - y)^2 = (x + y)^2 - 4xy = 3^2 - 4(\frac{5}{4}) = 9 - 5 = 4$.Thus,$x - y = 2$.Solving the system $x + y = 3$ and $x - y = 2$,we get $2x = 5 \implies x = \frac{5}{2}$ and $2y = 1 \implies y = \frac{1}{2}$.Therefore,$\sqrt{3 + \sqrt{5}} = \sqrt{\frac{5}{2}} + \sqrt{\frac{1}{2}} = \frac{\sqrt{5} + 1}{\sqrt{2}}$.

$\sqrt{3 + \sqrt{5}}$ is equal to

Similar Questions

The value of $\sqrt{12\sqrt{5} + 2\sqrt{55}}$ is:

What is the square root of $\sqrt{50} + \sqrt{48}$?

The cube root of $9\sqrt{3} + 11\sqrt{2}$ is

The value of $\sqrt{12 - \sqrt{68 + 48\sqrt{2}}}$ is:

$\sinh^{-1}\left(2^{3/2}\right)$ is equal to :

Vedclass Test Series

Exam Paper Generator

Online Exam Module