Solve 2*3*14sqrt{5/10}

$$2 \cdot 3 \cdot 14 \sqrt{ \frac{ 5 }{ 10 } }$$

Evaluate

$$42\sqrt{2}\approx 59.39696962$$

Solution Steps

Multiply 2 and 3 to get 6.

$$6\times 14\sqrt{\frac{5}{10}}$$

Multiply 6 and 14 to get 84.

$$84\sqrt{\frac{5}{10}}$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$84\sqrt{\frac{1}{2}}$$

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

$$84\times \frac{\sqrt{1}}{\sqrt{2}}$$

Calculate the square root of 1 and get 1.

$$84\times \frac{1}{\sqrt{2}}$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$84\times \frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$84\times \frac{\sqrt{2}}{2}$$

Cancel out 2, the greatest common factor in 84 and 2.

$$42\sqrt{2}$$