Simplify ( square root of 32x^6y^10)/( square root of x)

$\frac{\sqrt{32 x^{6} y^{10}}}{\sqrt{x}}$

Step 1

Combine $\sqrt{32 x^{6} y^{10}}$ and $\sqrt{x}$ into a single radical.

$\sqrt{\frac{32 x^{6} y^{10}}{x}}$

Step 2

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{32 x^{6} y^{10}}{x}$ by cancelling the common factors.

Factor $x$ out of $32 x^{6} y^{10}$ .

$\sqrt{\frac{x (32 x^{5} y^{10})}{x}}$

Raise $x$ to the power of $1$ .

$\sqrt{\frac{x (32 x^{5} y^{10})}{x^{1}}}$

Factor $x$ out of $x^{1}$ .

$\sqrt{\frac{x (32 x^{5} y^{10})}{x \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{x (32 x^{5} y^{10})}{x \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{32 x^{5} y^{10}}{1}}$

Divide $32 x^{5} y^{10}$ by $1$ .

$\sqrt{32 x^{5} y^{10}}$

Step 3

Rewrite $32 x^{5} y^{10}$ as ${(4 x^{2} y^{5})}^{2} \cdot (2 x)$ .

Factor $16$ out of $32$ .

$\sqrt{16 (2) x^{5} y^{10}}$

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 2 x^{5} y^{10}}$

Factor out $x^{4}$ .

$\sqrt{4^{2} \cdot 2 (x^{4} x) y^{10}}$

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

$\sqrt{4^{2} \cdot 2 ({(x^{2})}^{2} x) y^{10}}$

Rewrite $y^{10}$ as ${(y^{5})}^{2}$ .

$\sqrt{4^{2} \cdot 2 ({(x^{2})}^{2} x) {(y^{5})}^{2}}$

Move $x$ .

$\sqrt{4^{2} \cdot 2 ({(x^{2})}^{2}) {(y^{5})}^{2} x}$

Move $2$ .

$\sqrt{4^{2} ({(x^{2})}^{2}) {(y^{5})}^{2} \cdot 2 x}$

Rewrite $(4^{2} ({(x^{2})}^{2})) {(y^{5})}^{2}$ as ${(4 x^{2} y^{5})}^{2}$ .

$\sqrt{{(4 x^{2} y^{5})}^{2} \cdot 2 x}$

Add parentheses.

$\sqrt{{(4 x^{2} y^{5})}^{2} \cdot (2 x)}$

Step 4

Pull terms out from under the radical.

$4 x^{2} y^{5} \sqrt{2 x}$