Chapter 9.2, Problem 28E

To determine

The prime factorization of 450 to write square root of 450 in simplest form

Answer to Problem 28E

  $15\sqrt{2}$

Explanation of Solution

Given:

The given expression is

  $\sqrt{450}$

Calculation:

Firstly, we will divide 450 by 2 i.e. the prime number, we get 225 as the quotient. Now, divide 225 by the next prime number i.e. 3, we get 75 as quotient. Divide 75 by 3 again, we get 25 as quotient. Next, divide 25 by 5, the next prime number by which 25 is divisible. We get 5 as quotient. Again divide 5 by 5, we get 1 as quotient.

  $\begin{array}{l}=450\\ =2\times 3\times 3\times 5\times 5\\ Now,\sqrt{450}\\ =\sqrt{2\times 3\times 3\times 5\times 5}\\ =\left(3\times 5\right)\sqrt{2}\\ =15\sqrt{2}\end{array}$