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Expert-verified Found in: Page 1077 ### Elementary Algebra

Book edition 2nd
Author(s) Lynn Marecek, MaryAnne Anthony-Smith
Pages 1240 pages
ISBN 9780998625713 # In the following exercises, simplify.$\left(\sqrt{35{y}^{3}}\right)\left(\sqrt{7{y}^{3}}\right)$

The simplified form of the given expression is $7\sqrt{5}{y}^{3}$.

See the step by step solution

## Step 1. Given information.

The given expression is:

$\left(\sqrt{35{y}^{3}}\right)\left(\sqrt{7{y}^{3}}\right)$

## Step 2. Determine the simplified form.

The given expression can be written as:

$\begin{array}{rcl}\left(\sqrt{35{y}^{3}}\right)\left(\sqrt{7{y}^{3}}\right)& =& \sqrt{\left(35·7\right)·\left({y}^{3}·{y}^{3}\right)}\\ & =& \sqrt{\left(245\right)·\left({y}^{6}\right)}\\ & =& \sqrt{49}·\sqrt{5}·\sqrt{{y}^{6}}\\ & =& 7·\sqrt{5}·{y}^{3}\\ & =& 7\sqrt{5}{y}^{3}\end{array}$

## Step 3. Conclusion.

The simplified form of the given expression is $7\sqrt{5}{y}^{3}$. ### Want to see more solutions like these? 