Simplify the Radical Expression 4 square root of 60a^6b

$4 \sqrt{60 a^{6} b}$

Step 1

Rewrite $60 a^{6} b$ as ${(2 a^{3})}^{2} \cdot (15 b)$ .

Factor $4$ out of $60$ .

$4 \sqrt{4 (15) a^{6} b}$

Rewrite $4$ as $2^{2}$ .

$4 \sqrt{2^{2} \cdot 15 a^{6} b}$

Rewrite $a^{6}$ as ${(a^{3})}^{2}$ .

$4 \sqrt{2^{2} \cdot 15 {(a^{3})}^{2} b}$

Move $15$ .

$4 \sqrt{2^{2} {(a^{3})}^{2} \cdot 15 b}$

Rewrite $2^{2} {(a^{3})}^{2}$ as ${(2 a^{3})}^{2}$ .

$4 \sqrt{{(2 a^{3})}^{2} \cdot 15 b}$

Add parentheses.

$4 \sqrt{{(2 a^{3})}^{2} \cdot (15 b)}$

Step 2

Pull terms out from under the radical.

$4 (| 2 a^{3} | \sqrt{15 b})$

Step 3

Remove non-negative terms from the absolute value.

$4 (2 | a^{3} | \sqrt{15 b})$

Step 4

Multiply $2$ by $4$ .

$8 | a^{3} | \sqrt{15 b}$