Question

Rewrite the following expression so it does not contain any radical term

Answer 1

Given:

The expression is given as,

`\sqrt[]{36p^(10)m^6}`

The objective is to rewrite the expression without any radical form.

Step-by-step explanation:

The given expression can be written as,

`\sqrt[]{36p^(10)m^6}=\sqrt[]{6^2p^(10)m^6}\text{ . . . . .(1)}`

In general, the radical form of a square root can be written as,

`\sqrt[]{x}=x^{(1)/(2)}`

Then, the equation (1) can be written as

`\sqrt[]{36p^(10)m^6}=(6^2p^(10)m^6)^{(1)/(2)}`

On further solving the above expression,

`\begin{gathered} \sqrt[]{36p^(10)m^6}=6^{2*(1)/(2)}p^{10*(1)/(2)}m^{6*(1)/(2)} \\ =6p^5m^3 \end{gathered}`

Hence, the simplified expression of the given term is,

`6p^5m^3`