Write the Fraction in Simplest Form square root of 16/15-1/3

$\sqrt{\frac{16}{15}} - \frac{1}{3}$

Rewrite $\sqrt{\frac{16}{15}}$ as $\frac{\sqrt{16}}{\sqrt{15}}$ .

$\frac{\sqrt{16}}{\sqrt{15}} - \frac{1}{3}$

Simplify the numerator.

Rewrite $16$ as $4^{2}$ .

$\frac{\sqrt{4^{2}}}{\sqrt{15}} - \frac{1}{3}$

Pull terms out from under the radical, assuming positive real numbers.

$\frac{4}{\sqrt{15}} - \frac{1}{3}$

Multiply $\frac{4}{\sqrt{15}}$ by $\frac{\sqrt{15}}{\sqrt{15}}$ .

$\frac{4}{\sqrt{15}} \cdot \frac{\sqrt{15}}{\sqrt{15}} - \frac{1}{3}$

Combine and simplify the denominator.

Multiply $\frac{4}{\sqrt{15}}$ by $\frac{\sqrt{15}}{\sqrt{15}}$ .

$\frac{4 \sqrt{15}}{\sqrt{15} \sqrt{15}} - \frac{1}{3}$

Raise $\sqrt{15}$ to the power of $1$ .

$\frac{4 \sqrt{15}}{{\sqrt{15}}^{1} \sqrt{15}} - \frac{1}{3}$

Raise $\sqrt{15}$ to the power of $1$ .

$\frac{4 \sqrt{15}}{{\sqrt{15}}^{1} {\sqrt{15}}^{1}} - \frac{1}{3}$

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

$\frac{4 \sqrt{15}}{{\sqrt{15}}^{1 + 1}} - \frac{1}{3}$

Add $1$ and $1$ .

$\frac{4 \sqrt{15}}{{\sqrt{15}}^{2}} - \frac{1}{3}$

Rewrite ${\sqrt{15}}^{2}$ as $15$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{15}$ as $15^{\frac{1}{2}}$ .

$\frac{4 \sqrt{15}}{{(15^{\frac{1}{2}})}^{2}} - \frac{1}{3}$

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

$\frac{4 \sqrt{15}}{15^{\frac{1}{2} \cdot 2}} - \frac{1}{3}$

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

$\frac{4 \sqrt{15}}{15^{\frac{2}{2}}} - \frac{1}{3}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{4 \sqrt{15}}{15^{\frac{2}{2}}} - \frac{1}{3}$

Rewrite the expression.

$\frac{4 \sqrt{15}}{15^{1}} - \frac{1}{3}$

Evaluate the exponent.

$\frac{4 \sqrt{15}}{15} - \frac{1}{3}$