Question

Simplify the root below and leave your answer in the form \frac{a}{b} \sqrt[]{ \frac{405}{324} } Our value for a is AnswerOur value for a is Answer

Answer 1

We are asked to simplify the following expression

`\sqrt[]{(405)/(324)}`

Recall the quotient rule of radicands given by

`\sqrt[]{(a)/(b)}=\frac{\sqrt[]{a}}{\sqrt[]{b}}`

Applying the above rule to the given expression

`\sqrt[]{(405)/(324)}=\frac{\sqrt[]{405}}{\sqrt[]{324}}`

Notice that the square root of 324 is equal to 18

`\frac{\sqrt[]{405}}{\sqrt[]{324}}=\frac{\sqrt[]{405}}{18}`

Also, notice that we can break 405 into factors as

`\sqrt[]{405}=\sqrt[]{81*5}=\sqrt[]{81}\cdot\sqrt[]{5}=9\cdot\sqrt[]{5}`

So, the expression becomes

`\frac{\sqrt[]{405}}{18}=\frac{9\cdot\sqrt[]{5}}{18}=\frac{\sqrt[]{5}}{2}`

Therefore, the simplified expression is

`\frac{\sqrt[]{5}}{2}`

a = √5

b = 2