Question

Evaluate the expression.

$\sqrt{2}\sqrt{50}$

Short answer

Answer is 10.

Step-by-step solution

Step 1. Factorize the terms in root into prime numbers.

$\sqrt{2}\sqrt{50}=\sqrt{2}\sqrt{2\times 5\times 5}$

Step 2. Re write the expression after combining common numbers.

$\sqrt{2}\sqrt{2\times 5\times 5}=\sqrt{2\times 2\times 5\times 5}$

Step 3. Simplify the expression by solving the square root.

$\begin{array}{c}\sqrt{2\times 2\times 5\times 5}=2\times 5\\ =10\end{array}$