Solve sqrt{18}divsqrt{3/4}*sqrt{4/3}

$$\sqrt{ 18 } \div \sqrt{ \frac{ 3 }{ 4 } } \times \sqrt{ \frac{ 4 }{ 3 } }$$

Evaluate

$$4\sqrt{2}\approx 5.656854249$$

Solution Steps

Rewrite the division of square roots \frac{\sqrt{18}}{\sqrt{\frac{3}{4}}} as the square root of the division \sqrt{\frac{18}{\frac{3}{4}}} and perform the division.

$$\sqrt{6}\sqrt{\frac{4}{3}}$$

Rewrite the square root of the division \sqrt{\frac{4}{3}} as the division of square roots \frac{\sqrt{4}}{\sqrt{3}}.

$$\sqrt{6}\times \frac{\sqrt{4}}{\sqrt{3}}$$

Calculate the square root of 4 and get 2.

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

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

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

The square of \sqrt{3} is 3.

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

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

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

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}.

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

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

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

Multiply 3 and 2 to get 6.

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

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

$$2\sqrt{2}$$