Question

SimplifyV63STEP 1: Write 63 as the product of a perfect-square factor and a factor that does not contain a perfect square.V63 =STEP 2: Use the Product Property of Radicals to write the expression as the product of two square roots.✓STEP 3: Take the square root of the perfect square,VAdditional MaterialseBook

Answer 1

STEP1

To write 63 as a product of a perfect-square factor and a factor that does not contain a perfect square, we would need to find all the prime factors.

The number 63 is a composite number. Now let us find the prime factors associated with 63.

The first step is to divide the number 63 with the smallest prime factor,i.e. 2.

63 ÷ 2 = 31.5; fraction cannot be a factor. Therefore, moving to the next prime number

Divide 63 by 3.

63 ÷ 3 = 21

Again divide 21 by 3 and keep on diving the output by 3 till you get 1 or a fraction.

21 ÷ 3 = 7

7 ÷ 3 = 2.33; cannot be a factor. Now move to the next prime number 7.

Dividing 7 by 7 we get,

7 ÷ 7 = 1

We have received 1 at the end and it doesn’t have any factor. Therefore, we cannot proceed further with the division method. the prime factorization of 63 is 3 × 3 × 7

Therefore, the answer to step 1 is

`9*7`

STEP 2

Rewrite the radicand as a product using the largest perfect square factor. This give

`\begin{gathered} \sqrt[]{63}=\sqrt[]{9}*\sqrt[]{7} \\ 9\text{ is the }largestperfectsquarefactor\text{ gotten from the previous step.} \end{gathered}`

STEP 3

The perfect square is 9. The square root of the perfect square is:

`\begin{gathered} \sqrt[]{9}=\sqrt[]{3*3} \\ =3 \end{gathered}`