Question

Explain how to use the product property of square roots to simplify the expression$\sqrt{700}$.

Short answer

The simplified value is$10\sqrt{7}$.

Step-by-step solution

Step 1. Given Information.

The given expression is$\sqrt{700}$.

Step 2. Calculation.

According to the Product Property of square roots,

$\sqrt{ab}=\sqrt{a}\times \sqrt{b}$

The given term can be simplified by using the Product Property of square roots as:

$\begin{array}{c}\sqrt{700}=\sqrt{7}\times \sqrt{100}\\ =\sqrt{7}\times {\left({10}^2\right)}^{\frac{1}{2}}\\ =\sqrt{7}\times 10\\ =10\sqrt{7}\end{array}$

Step 3. Conclusion.

The simplified value of the given expression is$10\sqrt{7}$.