Basic Math Examples

$\sqrt{5 y} \cdot \sqrt{15 y}$

Step 1

Multiply $\sqrt{5 y} \sqrt{15 y}$ .

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Step 1.1

Combine using the product rule for radicals.

$\sqrt{5 y (15 y)}$

Step 1.2

Multiply $15$ by $5$ .

$\sqrt{75 y \cdot y}$

Step 1.3

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

$\sqrt{75 (y^{1} y)}$

Step 1.4

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

$\sqrt{75 (y^{1} y^{1})}$

Step 1.5

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

$\sqrt{75 y^{1 + 1}}$

Step 1.6

Add $1$ and $1$ .

$\sqrt{75 y^{2}}$

$\sqrt{75 y^{2}}$

Step 2

Rewrite $75 y^{2}$ as ${(5 y)}^{2} \cdot 3$ .

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Step 2.1

Factor $25$ out of $75$ .

$\sqrt{25 (3) y^{2}}$

Step 2.2

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

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

Step 2.3

Move $3$ .

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

Step 2.4

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

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

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

Step 3

Pull terms out from under the radical.

$5 y \sqrt{3}$

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