Simplify (4- square root of 3)/( square root of 5)

$\frac{4 - \sqrt{3}}{\sqrt{5}}$

Step 1

Multiply $\frac{4 - \sqrt{3}}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$\frac{4 - \sqrt{3}}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}$

Step 2

Combine and simplify the denominator.

Multiply $\frac{4 - \sqrt{3}}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$\frac{(4 - \sqrt{3}) \sqrt{5}}{\sqrt{5} \sqrt{5}}$

Raise $\sqrt{5}$ to the power of $1$ .

$\frac{(4 - \sqrt{3}) \sqrt{5}}{{\sqrt{5}}^{1} \sqrt{5}}$

Raise $\sqrt{5}$ to the power of $1$ .

$\frac{(4 - \sqrt{3}) \sqrt{5}}{{\sqrt{5}}^{1} {\sqrt{5}}^{1}}$

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

$\frac{(4 - \sqrt{3}) \sqrt{5}}{{\sqrt{5}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{(4 - \sqrt{3}) \sqrt{5}}{{\sqrt{5}}^{2}}$

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$\frac{(4 - \sqrt{3}) \sqrt{5}}{{(5^{\frac{1}{2}})}^{2}}$

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

$\frac{(4 - \sqrt{3}) \sqrt{5}}{5^{\frac{1}{2} \cdot 2}}$

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

$\frac{(4 - \sqrt{3}) \sqrt{5}}{5^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{(4 - \sqrt{3}) \sqrt{5}}{5^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{(4 - \sqrt{3}) \sqrt{5}}{5^{1}}$

Evaluate the exponent.

$\frac{(4 - \sqrt{3}) \sqrt{5}}{5}$

Step 3

Apply the distributive property.

$\frac{4 \sqrt{5} - \sqrt{3} \sqrt{5}}{5}$

Step 4

Multiply $- \sqrt{3} \sqrt{5}$ .

Combine using the product rule for radicals.

$\frac{4 \sqrt{5} - \sqrt{5 \cdot 3}}{5}$

Multiply $5$ by $3$ .

$\frac{4 \sqrt{5} - \sqrt{15}}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{4 \sqrt{5} - \sqrt{15}}{5}$

Decimal Form:

$1.01425771 \dots$