Solve sqrt{4*3*9^4/14}

$$\sqrt { \frac { 4 \times 3 \cdot 9 ^ { 4 } } { 14 } }$$

Evaluate

$$\frac{81\sqrt{42}}{7}\approx 74.991428082$$

Solution Steps

Multiply 4 and 3 to get 12.

$$\sqrt{\frac{12\times 9^{4}}{14}}$$

Calculate 9 to the power of 4 and get 6561.

$$\sqrt{\frac{12\times 6561}{14}}$$

Multiply 12 and 6561 to get 78732.

$$\sqrt{\frac{78732}{14}}$$

Reduce the fraction \frac{78732}{14} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{39366}{7}}$$

Rewrite the square root of the division \sqrt{\frac{39366}{7}} as the division of square roots \frac{\sqrt{39366}}{\sqrt{7}}.

$$\frac{\sqrt{39366}}{\sqrt{7}}$$

Factor 39366=81^{2}\times 6. Rewrite the square root of the product \sqrt{81^{2}\times 6} as the product of square roots \sqrt{81^{2}}\sqrt{6}. Take the square root of 81^{2}.

$$\frac{81\sqrt{6}}{\sqrt{7}}$$

Rationalize the denominator of \frac{81\sqrt{6}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{81\sqrt{6}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{81\sqrt{6}\sqrt{7}}{7}$$

To multiply \sqrt{6} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{81\sqrt{42}}{7}$$