Solve sqrt{3^3/(4+2)^4}=

$$\sqrt { \frac { 3 ^ { 3 } } { ( 4 + 2 ) ^ { 4 } } } =$$

Evaluate

$$\frac{\sqrt{3}}{12}\approx 0.144337567$$

Solution Steps

Calculate 3 to the power of 3 and get 27.

$$\sqrt{\frac{27}{\left(4+2\right)^{4}}}$$

Add 4 and 2 to get 6.

$$\sqrt{\frac{27}{6^{4}}}$$

Calculate 6 to the power of 4 and get 1296.

$$\sqrt{\frac{27}{1296}}$$

Reduce the fraction \frac{27}{1296} to lowest terms by extracting and canceling out 27.

$$\sqrt{\frac{1}{48}}$$

Rewrite the square root of the division \sqrt{\frac{1}{48}} as the division of square roots \frac{\sqrt{1}}{\sqrt{48}}.

$$\frac{\sqrt{1}}{\sqrt{48}}$$

Calculate the square root of 1 and get 1.

$$\frac{1}{\sqrt{48}}$$

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

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

Rationalize the denominator of \frac{1}{4\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{3}}{4\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{3}}{4\times 3}$$

Multiply 4 and 3 to get 12.

$$\frac{\sqrt{3}}{12}$$