Solve 1016/sqrt{2*10*10}

$$\frac{ 1016 }{ \sqrt{ 2 } \times 10 \times 10 }$$

Evaluate

$$\frac{127\sqrt{2}}{25}\approx 7.184204897$$

Solution Steps

Multiply 10 and 10 to get 100.

$$\frac{1016}{100\sqrt{2}}$$

Rationalize the denominator of \frac{1016}{100\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{1016\sqrt{2}}{100\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{1016\sqrt{2}}{100\times 2}$$

Cancel out 2\times 4 in both numerator and denominator.

$$\frac{127\sqrt{2}}{25}$$