Simplify square root of 98x^4y^6z^2

$\sqrt{98 x^{4} y^{6} z^{2}}$

Step 1

Rewrite $98 x^{4} y^{6} z^{2}$ as ${(7 x^{2} y^{3} z)}^{2} \cdot 2$ .

Factor $49$ out of $98$ .

$\sqrt{49 (2) x^{4} y^{6} z^{2}}$

Rewrite $49$ as $7^{2}$ .

$\sqrt{7^{2} \cdot 2 x^{4} y^{6} z^{2}}$

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

$\sqrt{7^{2} \cdot 2 {(x^{2})}^{2} y^{6} z^{2}}$

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

$\sqrt{7^{2} \cdot 2 {(x^{2})}^{2} {(y^{3})}^{2} z^{2}}$

Move $2$ .

$\sqrt{7^{2} {(x^{2})}^{2} {(y^{3})}^{2} z^{2} \cdot 2}$

Rewrite $7^{2} {(x^{2})}^{2} {(y^{3})}^{2} z^{2}$ as ${(7 x^{2} y^{3} z)}^{2}$ .

$\sqrt{{(7 x^{2} y^{3} z)}^{2} \cdot 2}$

Step 2

Pull terms out from under the radical.

$7 x^{2} y^{3} z \sqrt{2}$