Question

Evaluate the expression.

${\mathbf{2}}^{1/2}{\mathbf{8}}^{1/2}$

Short answer

Answer is 4.

Step-by-step solution

Step 1. Understanding the concept of square roots.

In order to solve the expression we shall prime factorize the numbers in the root and shall take out the pairs out of the root.

Step 2. Factorizing the given numbers.

${\text{2}}^{\text{1/2}}{\text{8}}^{\text{1/2}}\text{=}\left(\sqrt{\text{2}}\right)\left(\sqrt{\text{2×2×2}}\right)$

Step 3. Solving the expression.

$\begin{array}{c}\left(\sqrt{\text{2}}\right)\left(\sqrt{\text{2×2×2}}\right)\text{=}\sqrt{\text{2}}\text{×2}\sqrt{\text{2}}\\ \text{=2×2}\\ \text{=4}\end{array}$