Simplify square root of 42a^4b^6

$\sqrt{42 a^{4} b^{6}}$

Step 1

Rewrite $42 a^{4} b^{6}$ as ${(a^{2} b^{3})}^{2} \cdot 42$ .

Rewrite $a^{4}$ as ${(a^{2})}^{2}$ .

$\sqrt{42 {(a^{2})}^{2} b^{6}}$

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

$\sqrt{42 {(a^{2})}^{2} {(b^{3})}^{2}}$

Move $42$ .

$\sqrt{{(a^{2})}^{2} {(b^{3})}^{2} \cdot 42}$

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

$\sqrt{{(a^{2} b^{3})}^{2} \cdot 42}$

Step 2

Pull terms out from under the radical.

$a^{2} b^{3} \sqrt{42}$