Question

simplify.
\sqrt{343}

Explanation:

Step1: Factor 343 into prime components

$343 = 7 \times 7 \times 7 = 7^2 \times 7$

Step2: Separate perfect square factor

$\sqrt{343} = \sqrt{7^2 \times 7}$

Step3: Simplify the square root

$\sqrt{7^2 \times 7} = \sqrt{7^2} \times \sqrt{7} = 7\sqrt{7}$

Answer:

$7\sqrt{7}$