Question

Simplify:$\left(a\right)\sqrt{169y^2}\left(b\right)-\sqrt{121y^2}$

Short answer

The solution of (a) and (b) are$13\left|y\right|and-11\left|y\right|$ respectively.

Step-by-step solution

Part (a) Step 1. Given information

The root:$\sqrt{169y^2}$

Part (a) Step 2. Calculation

We have,

$$\begin{gathered} \sqrt{169y^2} \\ =\sqrt{{\left(13y\right)}^2}\sin ce{\left(13y\right)}^2=169y^2 \\ =13\left|y\right|\sin cetheindexniseven,\sqrt[n]{a^n}=\left|a\right| \end{gathered}$$

Therefore, the solution is$13\left|y\right|$

Part (b) Step 1. Given information

The root:$-\sqrt{121y^2}$

Part (b) Step 2. Calculation

We have,

$$\begin{gathered} -\sqrt{121y^2} \\ =-\sqrt{{\left(11y\right)}^2}\sin ce{\left(11y\right)}^2=121y^2 \\ =-11\left|y\right|\sin cetheindexniseven,\sqrt[n]{a^n}=\left|a\right| \end{gathered}$$

Therefore, the solution is$-11\left|y\right|$