Solve 98sqrt{1/8}56sqrt{5/8}

$$98 \sqrt{ \frac{ 1 }{ 8 } } 56 \sqrt{ \frac{ 5 }{ 8 } }$$

Evaluate

$$686\sqrt{5}\approx 1533.942632565$$

Solution Steps

To multiply \sqrt{\frac{1}{8}} and \sqrt{\frac{5}{8}}, multiply the numbers under the square root.

$$56\times 98\sqrt{\frac{5}{64}}$$

Multiply 56 and 98 to get 5488.

$$5488\sqrt{\frac{5}{64}}$$

Rewrite the square root of the division \sqrt{\frac{5}{64}} as the division of square roots \frac{\sqrt{5}}{\sqrt{64}}.

$$5488\times \frac{\sqrt{5}}{\sqrt{64}}$$

Calculate the square root of 64 and get 8.

$$5488\times \frac{\sqrt{5}}{8}$$

Cancel out 8, the greatest common factor in 5488 and 8.

$$686\sqrt{5}$$