Solve frac{sqrt{48}}{sqrt{64}}*2/sqrt{3}=

$$\frac { \sqrt { 48 } } { \sqrt { 64 } } \times \frac { 2 } { \sqrt { 3 } } =$$

Evaluate

$$1$$

Solution Steps

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$\frac{4\sqrt{3}}{\sqrt{64}}\times \frac{2}{\sqrt{3}}$$

Calculate the square root of 64 and get 8.

$$\frac{4\sqrt{3}}{8}\times \frac{2}{\sqrt{3}}$$

Divide 4\sqrt{3} by 8 to get \frac{1}{2}\sqrt{3}.

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

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

$$\frac{1}{2}\sqrt{3}\times \frac{2\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

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

Multiply \frac{1}{2} times \frac{2\sqrt{3}}{3} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 2 in both numerator and denominator.

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

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

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

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

$$\frac{3}{3}$$

Divide 3 by 3 to get 1.

$$1$$

Factor

$$1$$