simplify. 5\\sqrt{147}

Explanation:

Step1: Prime - factorize 147

$147 = 3\times7\times7$

Step2: Rewrite the square - root

$5\sqrt{147}=5\sqrt{3\times7^{2}}$

Step3: Use the square - root property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ ($a = 3$, $b = 7^{2}$)

$5\sqrt{3\times7^{2}}=5\times\sqrt{3}\times\sqrt{7^{2}}$

Step4: Simplify $\sqrt{7^{2}}$

Since $\sqrt{7^{2}} = 7$, then $5\times\sqrt{3}\times\sqrt{7^{2}}=5\times7\times\sqrt{3}$

Step5: Calculate the product

$5\times7\times\sqrt{3}=35\sqrt{3}$

Answer:

$35\sqrt{3}$