Question

Which choice is equivalent to the expression below? 45 + 125 O A. 25 B. 8-15 C. v5 D. 8.16

Answer 1

The given expression is :

`\sqrt[]{45}+\sqrt[]{125}`

The expression for the square root is :

`\sqrt[]{a^2}=a`

In the given expression, simplify one by one :

`\begin{gathered} \sqrt[]{45}\text{ } \\ \text{Factors of 45 = 5}*3*3 \\ \sqrt[]{45}\text{ =}\sqrt[]{5*3*3} \\ \sqrt[]{45}=\sqrt[]{5*3^2} \\ \sqrt[]{45}=3\sqrt[]{5} \end{gathered}`

Now :

`\begin{gathered} \sqrt[]{125}\colon \\ \text{factors of 125 = 5}*5*5 \\ \sqrt[]{125}=\sqrt[]{5*5*5} \\ \sqrt[]{125}=\sqrt[]{5*5^2} \\ \sqrt[]{125}=5\sqrt[]{5} \end{gathered}`

Substitute the value in the expression and simplify :

`\begin{gathered} \sqrt[]{45}+\sqrt[]{125}=3\sqrt[]{5}+5\sqrt[]{5} \\ \sqrt[]{45}+\sqrt[]{125}=(3+5)\sqrt[]{5} \\ \sqrt[]{45}+\sqrt[]{125}=8\sqrt[]{5} \end{gathered}`

Answer : B)

`8\sqrt[]{5}`