Solve 55^2sqrt{56/36}

$${ 55 }^{ 2 } \sqrt{ \frac{ 56 }{ 36 } }$$

Evaluate

$$\frac{3025\sqrt{14}}{3}\approx 3772.837864997$$

Solution Steps

Calculate 55 to the power of 2 and get 3025.

$$3025\sqrt{\frac{56}{36}}$$

Reduce the fraction \frac{56}{36} to lowest terms by extracting and canceling out 4.

$$3025\sqrt{\frac{14}{9}}$$

Rewrite the square root of the division \sqrt{\frac{14}{9}} as the division of square roots \frac{\sqrt{14}}{\sqrt{9}}.

$$3025\times \frac{\sqrt{14}}{\sqrt{9}}$$

Calculate the square root of 9 and get 3.

$$3025\times \frac{\sqrt{14}}{3}$$

Express 3025\times \frac{\sqrt{14}}{3} as a single fraction.

$$\frac{3025\sqrt{14}}{3}$$