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

Question

asked Jul 20, 2023 190k views

1 Answer

Nikhil Vartak · Answer 1 · 2023-07-26T17:57:16+0000

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,