Solve sqrt{27}div3/10sqrt{3/8}

$$\sqrt{ 27 } \div \frac{ 3 }{ 10 } \sqrt{ \frac{ 3 }{ 8 } }$$

Evaluate

$$\frac{15\sqrt{2}}{2}\approx 10.606601718$$

Solution Steps

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$\frac{3\sqrt{3}}{\frac{3}{10}}\sqrt{\frac{3}{8}}$$

Divide 3\sqrt{3} by \frac{3}{10} by multiplying 3\sqrt{3} by the reciprocal of \frac{3}{10}.

$$\frac{3\sqrt{3}\times 10}{3}\sqrt{\frac{3}{8}}$$

Cancel out 3 and 3.

$$\sqrt{3}\times 10\sqrt{\frac{3}{8}}$$

Rewrite the square root of the division \sqrt{\frac{3}{8}} as the division of square roots \frac{\sqrt{3}}{\sqrt{8}}.

$$\sqrt{3}\times 10\times \frac{\sqrt{3}}{\sqrt{8}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\sqrt{3}\times 10\times \frac{\sqrt{3}}{2\sqrt{2}}$$

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

$$\sqrt{3}\times 10\times \frac{\sqrt{3}\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\sqrt{3}\times 10\times \frac{\sqrt{3}\sqrt{2}}{2\times 2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$\sqrt{3}\times 10\times \frac{\sqrt{6}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\sqrt{3}\times 10\times \frac{\sqrt{6}}{4}$$

Express \sqrt{3}\times \frac{\sqrt{6}}{4} as a single fraction.

$$\frac{\sqrt{3}\sqrt{6}}{4}\times 10$$

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}.

$$\frac{\sqrt{3}\sqrt{3}\sqrt{2}}{4}\times 10$$

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

$$\frac{3\sqrt{2}}{4}\times 10$$

Express \frac{3\sqrt{2}}{4}\times 10 as a single fraction.

$$\frac{3\sqrt{2}\times 10}{4}$$

Multiply 3 and 10 to get 30.

$$\frac{30\sqrt{2}}{4}$$

Divide 30\sqrt{2} by 4 to get \frac{15}{2}\sqrt{2}.

$$\frac{15}{2}\sqrt{2}$$