Question

In the following exercises, simplify.

$\frac{15+\sqrt{75}}{5}$

Short answer

The required answer is$\left(3+\sqrt{3}\right)$.

Step-by-step solution

Step 1. Given information.

The given expression is:

$\frac{15+\sqrt{75}}{5}$

Step 2. Use the Product Property to Simplify Square Root.

$\frac{15+\sqrt{75}}{5}$

Rewrite the radicand as a product using the largest perfect square factor.

$\frac{15+\sqrt{25·3}}{5}$

Rewrite the radical as the product of two radicals.

$\frac{15+\sqrt{25}·\sqrt{3}}{5}$

Simplify,

$\frac{15+5\sqrt{3}}{5}$

Factor the common factor from the numerator,

$\frac{5\left(3+\sqrt{3}\right)}{5}$

Remove the common factor and simplify,

$\left(3+\sqrt{3}\right)$