Question

simplify.
$7\sqrt{363}$

Explanation:

Step1: Factor 363

Factorize 363 to find perfect square factors. $363 = 121\times3$, and $121 = 11^2$.

Step2: Simplify the square root

Using the property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ (for $a\geq0,b\geq0$), we have $\sqrt{363}=\sqrt{121\times3}=\sqrt{121}\cdot\sqrt{3}=11\sqrt{3}$.

Step3: Multiply by 7

Multiply the result by 7: $7\times11\sqrt{3}=77\sqrt{3}$.

Answer:

$77\sqrt{3}$