Algebra Examples

$\sqrt{6 x} \cdot \sqrt{15 x y} \cdot \sqrt{20}$

Step 1

Multiply $\sqrt{6 x} \sqrt{15 x y}$ .

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Step 1.1

Combine using the product rule for radicals.

$\sqrt{6 x (15 x y)} \cdot \sqrt{20}$

Step 1.2

Multiply $15$ by $6$ .

$\sqrt{90 x (x y)} \cdot \sqrt{20}$

Step 1.3

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

$\sqrt{90 (x^{1} x) y} \cdot \sqrt{20}$

Step 1.4

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

$\sqrt{90 (x^{1} x^{1}) y} \cdot \sqrt{20}$

Step 1.5

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

$\sqrt{90 x^{1 + 1} y} \cdot \sqrt{20}$

Step 1.6

Add $1$ and $1$ .

$\sqrt{90 x^{2} y} \cdot \sqrt{20}$

$\sqrt{90 x^{2} y} \cdot \sqrt{20}$

Step 2

Rewrite $90 x^{2} y$ as ${(3 x)}^{2} \cdot (10 y)$ .

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Step 2.1

Factor $9$ out of $90$ .

$\sqrt{9 (10) x^{2} y} \cdot \sqrt{20}$

Step 2.2

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

$\sqrt{3^{2} \cdot 10 x^{2} y} \cdot \sqrt{20}$

Step 2.3

Move $10$ .

$\sqrt{3^{2} x^{2} \cdot 10 y} \cdot \sqrt{20}$

Step 2.4

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

$\sqrt{{(3 x)}^{2} \cdot 10 y} \cdot \sqrt{20}$

Step 2.5

Add parentheses.

$\sqrt{{(3 x)}^{2} \cdot (10 y)} \cdot \sqrt{20}$

$\sqrt{{(3 x)}^{2} \cdot (10 y)} \cdot \sqrt{20}$

Step 3

Pull terms out from under the radical.

$3 x \sqrt{10 y} \cdot \sqrt{20}$

Step 4

Rewrite $20$ as $2^{2} \cdot 5$ .

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Step 4.1

Factor $4$ out of $20$ .

$3 x \sqrt{10 y} \cdot \sqrt{4 (5)}$

Step 4.2

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

$3 x \sqrt{10 y} \cdot \sqrt{2^{2} \cdot 5}$

$3 x \sqrt{10 y} \cdot \sqrt{2^{2} \cdot 5}$

Step 5

Pull terms out from under the radical.

$3 x \sqrt{10 y} \cdot (2 \sqrt{5})$

Step 6

Multiply $3 x \sqrt{10 y} (2 \sqrt{5})$ .

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Step 6.1

Multiply $2$ by $3$ .

$6 x \sqrt{10 y} \sqrt{5}$

Step 6.2

Combine using the product rule for radicals.

$6 x \sqrt{5 (10 y)}$

Step 6.3

Multiply $5$ by $10$ .

$6 x \sqrt{50 y}$

$6 x \sqrt{50 y}$

Step 7

Rewrite $50 y$ as $5^{2} \cdot (2 y)$ .

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Step 7.1

Factor $25$ out of $50$ .

$6 x \sqrt{25 (2) y}$

Step 7.2

Rewrite $25$ as $5^{2}$ .

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

Step 7.3

Add parentheses.

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

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

Step 8

Pull terms out from under the radical.

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

Step 9

Multiply $5$ by $6$ .

$30 x \sqrt{2 y}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$