Solve sqrt{288}sqrt{1/72}=

$$\sqrt{ 288 } \sqrt{ \frac{ 1 }{ 72 } } =$$

Evaluate

$$2$$

Solution Steps

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}.

$$12\sqrt{2}\sqrt{\frac{1}{72}}$$

Rewrite the square root of the division \sqrt{\frac{1}{72}} as the division of square roots \frac{\sqrt{1}}{\sqrt{72}}.

$$12\sqrt{2}\times \frac{\sqrt{1}}{\sqrt{72}}$$

Calculate the square root of 1 and get 1.

$$12\sqrt{2}\times \frac{1}{\sqrt{72}}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$12\sqrt{2}\times \frac{1}{6\sqrt{2}}$$

Rationalize the denominator of \frac{1}{6\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$12\sqrt{2}\times \frac{\sqrt{2}}{6\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$12\sqrt{2}\times \frac{\sqrt{2}}{6\times 2}$$

Multiply 6 and 2 to get 12.

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

Cancel out 12 and 12.

$$\sqrt{2}\sqrt{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$2$$

Factor

$$2$$