Question

Simplify the expression. $$\frac{\sqrt{10} \cdot \sqrt{16}}{\sqrt{5}}$$

Short answer

\(\sqrt{32}\)

Step-by-step solution

Separate the square roots

The first step is to apply the multiplication rule for square roots, which allows you to separate \(\sqrt{10} \cdot \sqrt{16}\) into \(\sqrt{10 \cdot 16}\) .

Simplify the Numerator

After the separation, you calculate \(10 \cdot 16\) which results to \(160\), thus the expression becomes \(\sqrt{160}/\sqrt{5}\).

Apply the rule to the denominator

Next, you apply the rule for division inside a square root which says the square root of a quotient is the quotient of square roots. Therefore, \(\sqrt{160}/\sqrt{5}\) could be expressed as \(\sqrt{160/5}\).

Simplify and calculate the remaining expression

Finally, calculate \(160/5\) which is \(32\), and take the square root of \(32\), which equals to \(\sqrt{32}\).