Find the square root of 24+2 sqrt{119}. | vedclass

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

Question

(C) To find the square root of $24+2 \sqrt{119}$,we assume that $\sqrt{24+2 \sqrt{119}} = \sqrt{x} + \sqrt{y}$.Squaring both sides,we get $24+2 \sqrt{

Vedclass · Accepted Answer

$\sqrt{17}+\sqrt{7}$

Vedclass · Answer

(C) To find the square root of $24+2 \sqrt{119}$,we assume that $\sqrt{24+2 \sqrt{119}} = \sqrt{x} + \sqrt{y}$.Squaring both sides,we get $24+2 \sqrt{119} = x + y + 2 \sqrt{xy}$.Comparing the rational and irrational parts,we have $x + y = 24$ and $xy = 119$.We need two numbers whose sum is $24$ and product is $119$.These numbers are $17$ and $7$,since $17+7=24$ and $17 	imes 7 = 119$.Therefore,$\sqrt{24+2 \sqrt{119}} = \sqrt{17} + \sqrt{7}$.

Find the square root of $24+2 \sqrt{119}$.

Similar Questions

$\sqrt{12}$ and ........ are like surds.

State whether the following rational number has a terminating decimal expansion or not. If it has,then find it: $\frac{23}{200}$

Express $96$ as a product of prime factors.

Find the largest number that divides $2053$ and $967$ and leaves a remainder of $5$ and $7$ respectively.

Prove that one and only one out of every three consecutive positive integers is divisible by $3$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module