Chapter 10.6, Problem 37E

To determine

To Simplify the expression

Answer to Problem 37E

  $\frac{2}{11}\sqrt{6}$

Explanation of Solution

Given information: $\sqrt{\frac{24}{121}}$

Formula Used: Prime Factorization

Calculation:

  $\sqrt{\frac{24}{121}}$

Now, Simplify by breaking into multiplication of prime numbers

  $\sqrt{\frac{24}{121}}=\sqrt{\frac{2\times 2\times 2\times 3}{11\times 11}}$

Now, pull out pair of prime numbers.

  $\sqrt{\frac{2\times 2\times 2\times 3}{11\times 11}}=\frac{2}{11}\sqrt{2\times 3}$

Hence, simplify

  $\sqrt{\frac{24}{121}}=\frac{2}{11}\sqrt{6}$