Simplify ( square root of 5)/( square root of 8x)

$\frac{\sqrt{5}}{\sqrt{8 x}}$

Step 1

Simplify the denominator.

Rewrite $8 x$ as $2^{2} \cdot (2 x)$ .

Factor $4$ out of $8$ .

$\frac{\sqrt{5}}{\sqrt{4 (2) x}}$

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

$\frac{\sqrt{5}}{\sqrt{2^{2} \cdot 2 x}}$

Add parentheses.

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

Pull terms out from under the radical.

$\frac{\sqrt{5}}{2 \sqrt{2 x}}$

Step 2

Multiply $\frac{\sqrt{5}}{2 \sqrt{2 x}}$ by $\frac{\sqrt{2 x}}{\sqrt{2 x}}$ .

$\frac{\sqrt{5}}{2 \sqrt{2 x}} \cdot \frac{\sqrt{2 x}}{\sqrt{2 x}}$

Step 3

Combine and simplify the denominator.

Multiply $\frac{\sqrt{5}}{2 \sqrt{2 x}}$ by $\frac{\sqrt{2 x}}{\sqrt{2 x}}$ .

$\frac{\sqrt{5} \sqrt{2 x}}{2 \sqrt{2 x} \sqrt{2 x}}$

Move $\sqrt{2 x}$ .

$\frac{\sqrt{5} \sqrt{2 x}}{2 (\sqrt{2 x} \sqrt{2 x})}$

Raise $\sqrt{2 x}$ to the power of $1$ .

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

Raise $\sqrt{2 x}$ to the power of $1$ .

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

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

$\frac{\sqrt{5} \sqrt{2 x}}{2 {\sqrt{2 x}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt{5} \sqrt{2 x}}{2 {\sqrt{2 x}}^{2}}$

Rewrite ${\sqrt{2 x}}^{2}$ as $2 x$ .

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

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

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

$\frac{\sqrt{5} \sqrt{2 x}}{2 {(2 x)}^{\frac{1}{2} \cdot 2}}$

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

$\frac{\sqrt{5} \sqrt{2 x}}{2 {(2 x)}^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{5} \sqrt{2 x}}{2 {(2 x)}^{\frac{2}{2}}}$

Rewrite the expression.

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

Simplify.

$\frac{\sqrt{5} \sqrt{2 x}}{2 (2 x)}$

Step 4

Simplify the numerator.

Combine using the product rule for radicals.

$\frac{\sqrt{5 (2 x)}}{2 \cdot 2 x}$

Multiply $5$ by $2$ .

$\frac{\sqrt{10 x}}{2 \cdot 2 x}$

Step 5

Multiply $2$ by $2$ .

$\frac{\sqrt{10 x}}{4 x}$

Simplify ( square root of 5)/( square root of 8x)

Related Questions

Support LCMGCF.com by disabling your adblocker.