Chapter 11.6, Problem 1MRE

To determine

To simplify: the given expression.

Answer to Problem 1MRE

  $\sqrt{16x^{16}{y}^2}=4x^{4}y$ .

Explanation of Solution

Given:

The given expression is $\sqrt{16x^{16}{y}^2}$ .

Calculation:

As the given expression is $\sqrt{16x^{16}{y}^2}$ .

Since, the factor of $16=2\times 2\times 2\times 2$ .

Therefore,

  $\begin{array}{l}\sqrt{16x^{16}{y}^2}=\sqrt{16}\times \sqrt{x^{16}}\times \sqrt{y^2}\\ =\sqrt{4^2}\times \sqrt{{\left(x^4\right)}^2}\times \sqrt{y^2}\left\{\text{simplify}\right\}\\ =4\times x^4\times y\{\because \sqrt{a^2}=a\}\\ \therefore \sqrt{16x^{16}{y}^2}=4x^{4}y\end{array}$

Hence, the simplified form of the given expression is $\sqrt{16x^{16}{y}^2}=4x^{4}y$ .