Solve 101600/2frac{1*10^2{sqrt{2}*6}}

$$\frac{ 101600 }{ 2 \frac{ 1 \times { 10 }^{ 2 } }{ \sqrt{ 2 } \times 6 } }$$

Evaluate

$$3048\sqrt{2}\approx 4310.522938113$$

Solution Steps

Calculate 10 to the power of 2 and get 100.

$$\frac{101600}{2\times \frac{1\times 100}{6\sqrt{2}}}$$

Multiply 1 and 100 to get 100.

$$\frac{101600}{2\times \frac{100}{6\sqrt{2}}}$$

Rationalize the denominator of \frac{100}{6\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{101600}{2\times \frac{100\sqrt{2}}{6\left(\sqrt{2}\right)^{2}}}$$

The square of \sqrt{2} is 2.

$$\frac{101600}{2\times \frac{100\sqrt{2}}{6\times 2}}$$

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

$$\frac{101600}{2\times \frac{25\sqrt{2}}{3}}$$

Express 2\times \frac{25\sqrt{2}}{3} as a single fraction.

$$\frac{101600}{\frac{2\times 25\sqrt{2}}{3}}$$

Divide 101600 by \frac{2\times 25\sqrt{2}}{3} by multiplying 101600 by the reciprocal of \frac{2\times 25\sqrt{2}}{3}.

$$\frac{101600\times 3}{2\times 25\sqrt{2}}$$

Cancel out 2\times 25 in both numerator and denominator.

$$\frac{3\times 2032}{\sqrt{2}}$$

Rationalize the denominator of \frac{3\times 2032}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{3\times 2032\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{3\times 2032\sqrt{2}}{2}$$

Multiply 3 and 2032 to get 6096.

$$\frac{6096\sqrt{2}}{2}$$

Divide 6096\sqrt{2} by 2 to get 3048\sqrt{2}.

$$3048\sqrt{2}$$