Solve (-2+6)^2divsqrt{12/3}

$$( - 2 + 6 ) ^ { 2 } \div \sqrt { 1 \frac { 2 } { 3 } }$$

Evaluate

$$\frac{16\sqrt{15}}{5}\approx 12.393546708$$

Solution Steps

Add -2 and 6 to get 4.

$$\frac{4^{2}}{\sqrt{\frac{1\times 3+2}{3}}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16}{\sqrt{\frac{1\times 3+2}{3}}}$$

Multiply 1 and 3 to get 3.

$$\frac{16}{\sqrt{\frac{3+2}{3}}}$$

Add 3 and 2 to get 5.

$$\frac{16}{\sqrt{\frac{5}{3}}}$$

Rewrite the square root of the division \sqrt{\frac{5}{3}} as the division of square roots \frac{\sqrt{5}}{\sqrt{3}}.

$$\frac{16}{\frac{\sqrt{5}}{\sqrt{3}}}$$

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{16}{\frac{\sqrt{5}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}$$

The square of \sqrt{3} is 3.

$$\frac{16}{\frac{\sqrt{5}\sqrt{3}}{3}}$$

To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.

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

Divide 16 by \frac{\sqrt{15}}{3} by multiplying 16 by the reciprocal of \frac{\sqrt{15}}{3}.

$$\frac{16\times 3}{\sqrt{15}}$$

Rationalize the denominator of \frac{16\times 3}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\frac{16\times 3\sqrt{15}}{\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$\frac{16\times 3\sqrt{15}}{15}$$

Multiply 16 and 3 to get 48.

$$\frac{48\sqrt{15}}{15}$$

Divide 48\sqrt{15} by 15 to get \frac{16}{5}\sqrt{15}.

$$\frac{16}{5}\sqrt{15}$$