Question

Evaluate the expression.

$\frac{\sqrt{242}}{\sqrt{2}}$

Short answer

Answer is 11.

Step-by-step solution

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

$\frac{\sqrt{\text{242}}}{\sqrt{\text{2}}}\text{=}\frac{\sqrt{\text{2×11×11}}}{\sqrt{\text{2}}}$

Step 2. Re write the expression after cancelling the common terms in numerator and denominator.

$\frac{\sqrt{\cancel{\text{2}}\text{×11×11}}}{\sqrt{\cancel{\text{2}}}}\text{=}\sqrt{\text{11×11}}$

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

$\sqrt{\text{11×11}}\text{=11}$