Solve 0.5sqrt{8100-1/4}sqrt{64}

$$0.5 \sqrt{ 8100- \frac{ 1 }{ 4 } } \sqrt{ 64 }$$

Evaluate

$$2\sqrt{32399}\approx 359.994444402$$

Solution Steps

Convert 8100 to fraction \frac{32400}{4}.

$$0.5\sqrt{\frac{32400}{4}-\frac{1}{4}}\sqrt{64}$$

Since \frac{32400}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$0.5\sqrt{\frac{32400-1}{4}}\sqrt{64}$$

Subtract 1 from 32400 to get 32399.

$$0.5\sqrt{\frac{32399}{4}}\sqrt{64}$$

Rewrite the square root of the division \sqrt{\frac{32399}{4}} as the division of square roots \frac{\sqrt{32399}}{\sqrt{4}}.

$$0.5\times \frac{\sqrt{32399}}{\sqrt{4}}\sqrt{64}$$

Calculate the square root of 4 and get 2.

$$0.5\times \frac{\sqrt{32399}}{2}\sqrt{64}$$

Calculate the square root of 64 and get 8.

$$0.5\times \frac{\sqrt{32399}}{2}\times 8$$

Multiply 0.5 and 8 to get 4.

$$4\times \frac{\sqrt{32399}}{2}$$

Cancel out 2, the greatest common factor in 4 and 2.

$$2\sqrt{32399}$$