Question

In the following exercises, simplify.

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

Short answer

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

Step-by-step solution

Step 1. Given information.

The given expression is:

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

Step 2. Determine the simplified form.

The given expression can be written as:

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

Step 3. Conclusion.

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