Solve frac{2sqrt{36}}{5sqrt{288}}

$$\frac { 2 \sqrt { 36 } } { 5 \sqrt { 288 } }$$

Evaluate

$$\frac{\sqrt{2}}{10}\approx 0.141421356$$

Solution Steps

Calculate the square root of 36 and get 6.

$$\frac{2\times 6}{5\sqrt{288}}$$

Multiply 2 and 6 to get 12.

$$\frac{12}{5\sqrt{288}}$$

Factor 288=12^{2}\times 2. Rewrite the square root of the product \sqrt{12^{2}\times 2} as the product of square roots \sqrt{12^{2}}\sqrt{2}. Take the square root of 12^{2}.

$$\frac{12}{5\times 12\sqrt{2}}$$

Multiply 5 and 12 to get 60.

$$\frac{12}{60\sqrt{2}}$$

Rationalize the denominator of \frac{12}{60\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{12\sqrt{2}}{60\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{12\sqrt{2}}{60\times 2}$$

Cancel out 12 in both numerator and denominator.

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

Multiply 2 and 5 to get 10.

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