Simplify 5x^2y square root of 8x^7y^6

$5 x^{2} y \sqrt{8 x^{7} y^{6}}$

Step 1

Rewrite $8 x^{7} y^{6}$ as ${(2 x^{3} y^{3})}^{2} \cdot (2 x)$ .

Factor $4$ out of $8$ .

$5 x^{2} y \sqrt{4 (2) x^{7} y^{6}}$

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

$5 x^{2} y \sqrt{2^{2} \cdot 2 x^{7} y^{6}}$

Factor out $x^{6}$ .

$5 x^{2} y \sqrt{2^{2} \cdot 2 (x^{6} x) y^{6}}$

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

$5 x^{2} y \sqrt{2^{2} \cdot 2 ({(x^{3})}^{2} x) y^{6}}$

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

$5 x^{2} y \sqrt{2^{2} \cdot 2 ({(x^{3})}^{2} x) {(y^{3})}^{2}}$

Move $x$ .

$5 x^{2} y \sqrt{2^{2} \cdot 2 ({(x^{3})}^{2}) {(y^{3})}^{2} x}$

Move $2$ .

$5 x^{2} y \sqrt{(2^{2} ({(x^{3})}^{2})) {(y^{3})}^{2} \cdot 2 x}$

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

$5 x^{2} y \sqrt{{(2 x^{3} y^{3})}^{2} \cdot 2 x}$

Add parentheses.

$5 x^{2} y \sqrt{{(2 x^{3} y^{3})}^{2} \cdot (2 x)}$

Step 2

Pull terms out from under the radical.

$5 x^{2} y (2 x^{3} y^{3} \sqrt{2 x})$

Step 3

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$5 (x^{3} x^{2}) y (2 y^{3} \sqrt{2 x})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$5 x^{3 + 2} y (2 y^{3} \sqrt{2 x})$

Add $3$ and $2$ .

$5 x^{5} y (2 y^{3} \sqrt{2 x})$

Step 4

Multiply $y$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

$5 x^{5} (y^{3} y) (2 \sqrt{2 x})$

Multiply $y^{3}$ by $y$ .

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

$5 x^{5} (y^{3} y^{1}) (2 \sqrt{2 x})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$5 x^{5} y^{3 + 1} (2 \sqrt{2 x})$

Add $3$ and $1$ .

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

Step 5

Multiply $2$ by $5$ .

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

Simplify 5x^2y square root of 8x^7y^6

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