Chapter 9.4, Problem 1CYU

To determine

Find the value of x.

Answer to Problem 1CYU

  $x=\pm 9.38$

Explanation of Solution

Given Information: $x^2=88$

Formula Used: Prime Factorization

Calculation:

  $x^2=88$

Now, square root both sides.

  $x=\sqrt{88}$

Now, Simplify by breaking into multiplication of prime numbers

  $\sqrt{88}=\sqrt{2\times 2\times 2\times 11}$

Now, pull out pair of prime numbers.

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

Hence, simplify

  $\sqrt{88}=2\sqrt{22}$

Now put the value of x.

  $x=2\sqrt{22}$

Now,

  $x=2\pm \sqrt{22}$

Hence,

  $x=\pm 9.38$