Solve 360/23*5sqrt{2}

$$\frac { 360 } { 23 \times 5 \sqrt { 2 } }$$

Evaluate

$$\frac{36\sqrt{2}}{23}\approx 2.213551663$$

Solution Steps

Multiply 5 and 23 to get 115.

$$\frac{360}{115\sqrt{2}}$$

Rationalize the denominator of \frac{360}{115\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{360\sqrt{2}}{115\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{360\sqrt{2}}{115\times 2}$$

Cancel out 2\times 5 in both numerator and denominator.

$$\frac{36\sqrt{2}}{23}$$