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

Find the $g.c.d.$ (Greatest Common Divisor) of $75$ and $243$ using Euclid's division algorithm.

The $\text{g.c.d.}$ (greatest common divisor) of any two consecutive natural numbers is:

Can the number $6^{n}$,where $n$ is a natural number,end with the digit $5$? Give reasons.

Prove that $\sqrt{7}$ is an irrational number.

Write the denominator of the rational number $\frac{257}{5000}$ in the form $2^{m} \times 5^{n},$ where $m, n$ are non-negative integers. Hence,write its decimal expansion,without actual division.

Vedclass Test Series

Exam Paper Generator

Online Exam Module