Simplify xy^2 square root of 45x^5y^5

$x y^{2} \sqrt{45 x^{5} y^{5}}$

Step 1

Rewrite $45 x^{5} y^{5}$ as ${(3 x^{2} y^{2})}^{2} \cdot (5 x y)$ .

Factor $9$ out of $45$ .

$x y^{2} \sqrt{9 (5) x^{5} y^{5}}$

Rewrite $9$ as $3^{2}$ .

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

Factor out $x^{4}$ .

$x y^{2} \sqrt{3^{2} \cdot 5 (x^{4} x) y^{5}}$

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

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

Factor out $y^{4}$ .

$x y^{2} \sqrt{3^{2} \cdot 5 ({(x^{2})}^{2} x) (y^{4} y)}$

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

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

Move $x$ .

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

Move $5$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

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

Move $x^{2}$ .

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

Multiply $x^{2}$ by $x$ .

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

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

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

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

Add $2$ and $1$ .

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

Step 5

Multiply $y^{2}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

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

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

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

Add $2$ and $2$ .

$3 x^{3} y^{4} \sqrt{5 x y}$

Simplify xy^2 square root of 45x^5y^5

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