Algebra Examples

$x \sqrt{63 x^{5} y^{7}}$

Step 1

Rewrite $63 x^{5} y^{7}$ as ${(3 x^{2} y^{3})}^{2} \cdot (7 x y)$ .

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Step 1.1

Factor $9$ out of $63$ .

$x \sqrt{9 (7) x^{5} y^{7}}$

Step 1.2

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

$x \sqrt{3^{2} \cdot 7 x^{5} y^{7}}$

Step 1.3

Factor out $x^{4}$ .

$x \sqrt{3^{2} \cdot 7 (x^{4} x) y^{7}}$

Step 1.4

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

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

Step 1.5

Factor out $y^{6}$ .

$x \sqrt{3^{2} \cdot 7 ({(x^{2})}^{2} x) (y^{6} y)}$

Step 1.6

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

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

Step 1.7

Move $x$ .

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

Step 1.8

Move $7$ .

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

Step 1.9

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

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

Step 1.10

Add parentheses.

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

Step 1.11

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

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

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Step 4.1

Move $x^{2}$ .

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

Step 4.2

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

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Step 4.2.1

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

$3 (x^{2} x^{1}) (y^{3} \sqrt{7 x y})$

Step 4.2.2

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

$3 x^{2 + 1} (y^{3} \sqrt{7 x y})$

Step 4.3

Add $2$ and $1$ .

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

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