Chapter 9.4, Problem 44PPS

To determine

Find the length.

Answer to Problem 44PPS

  $x=20$

Explanation of Solution

Given Information: $576={(x+4)}^2$

Formula Used: Prime Factorization

Calculation:

  $576={(x+4)}^2$

Now,

  ${(x+4)}^2=576$

Now, square root both sides.

  $x+4=\sqrt{576}$

Now, Simplify by breaking into multiplication of prime numbers

  $\sqrt{576}=\sqrt{2\times 2\times 2\times 2\times 2\times 2\times 3\times 3}$

Now, pull out the pair of prime numbers.

  $\sqrt{576}=2\times 2\times 2\times 3$

Hence,

  $\sqrt{576}=24$

Now put the value of $x+4$ .

  $x+4=24$

Now, simplify

  $x=24-4$

Hence,

  $x=20$