Solve sqrt{24}sqrt{1/3}

$$\sqrt{ 24 } \sqrt{ \frac{ 1 }{ 3 } }$$

Evaluate

$$2\sqrt{2}\approx 2.828427125$$

Solution Steps

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$2\sqrt{6}\sqrt{\frac{1}{3}}$$

Rewrite the square root of the division \sqrt{\frac{1}{3}} as the division of square roots \frac{\sqrt{1}}{\sqrt{3}}.

$$2\sqrt{6}\times \frac{\sqrt{1}}{\sqrt{3}}$$

Calculate the square root of 1 and get 1.

$$2\sqrt{6}\times \frac{1}{\sqrt{3}}$$

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$2\sqrt{6}\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$2\sqrt{6}\times \frac{\sqrt{3}}{3}$$

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

$$\frac{2\sqrt{3}}{3}\sqrt{6}$$

Express \frac{2\sqrt{3}}{3}\sqrt{6} as a single fraction.

$$\frac{2\sqrt{3}\sqrt{6}}{3}$$

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

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

Multiply 2 and 3 to get 6.

$$\frac{6\sqrt{2}}{3}$$

Divide 6\sqrt{2} by 3 to get 2\sqrt{2}.

$$2\sqrt{2}$$