Basic Math Examples

$\frac{\sqrt{8}}{\sqrt{h y}}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Rewrite $8$ as $2^{2} \cdot 2$ .

Tap for more steps...

Step 1.1.1

Factor $4$ out of $8$ .

$\frac{\sqrt{4 (2)}}{\sqrt{h y}}$

Step 1.1.2

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

$\frac{\sqrt{2^{2} \cdot 2}}{\sqrt{h y}}$

Step 1.2

Pull terms out from under the radical.

$\frac{2 \sqrt{2}}{\sqrt{h y}}$

Step 2

Multiply $\frac{2 \sqrt{2}}{\sqrt{h y}}$ by $\frac{\sqrt{h y}}{\sqrt{h y}}$ .

$\frac{2 \sqrt{2}}{\sqrt{h y}} \cdot \frac{\sqrt{h y}}{\sqrt{h y}}$

Step 3

Combine and simplify the denominator.

Tap for more steps...

Step 3.1

Multiply $\frac{2 \sqrt{2}}{\sqrt{h y}}$ by $\frac{\sqrt{h y}}{\sqrt{h y}}$ .

$\frac{2 \sqrt{2} \sqrt{h y}}{\sqrt{h y} \sqrt{h y}}$

Step 3.2

Raise $\sqrt{h y}$ to the power of $1$ .

$\frac{2 \sqrt{2} \sqrt{h y}}{{\sqrt{h y}}^{1} \sqrt{h y}}$

Step 3.3

Raise $\sqrt{h y}$ to the power of $1$ .

$\frac{2 \sqrt{2} \sqrt{h y}}{{\sqrt{h y}}^{1} {\sqrt{h y}}^{1}}$

Step 3.4

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

$\frac{2 \sqrt{2} \sqrt{h y}}{{\sqrt{h y}}^{1 + 1}}$

Step 3.5

Add $1$ and $1$ .

$\frac{2 \sqrt{2} \sqrt{h y}}{{\sqrt{h y}}^{2}}$

Step 3.6

Rewrite ${\sqrt{h y}}^{2}$ as $h y$ .

Tap for more steps...

Step 3.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{h y}$ as ${(h y)}^{\frac{1}{2}}$ .

$\frac{2 \sqrt{2} \sqrt{h y}}{{({(h y)}^{\frac{1}{2}})}^{2}}$

Step 3.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{2 \sqrt{2} \sqrt{h y}}{{(h y)}^{\frac{1}{2} \cdot 2}}$

Step 3.6.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{2 \sqrt{2} \sqrt{h y}}{{(h y)}^{\frac{2}{2}}}$

Step 3.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.6.4.1

Cancel the common factor.

$\frac{2 \sqrt{2} \sqrt{h y}}{{(h y)}^{\frac{2}{2}}}$

Step 3.6.4.2

Rewrite the expression.

$\frac{2 \sqrt{2} \sqrt{h y}}{{(h y)}^{1}}$

Step 3.6.5

Simplify.

$\frac{2 \sqrt{2} \sqrt{h y}}{h y}$

Step 4

Combine using the product rule for radicals.

$\frac{2 \sqrt{h y \cdot 2}}{h y}$

Step 5

Move $2$ to the left of $h y$ .

$\frac{2 \sqrt{2 h y}}{h y}$