Solve sqrt{21/2}div3sqrt{28}

$$\sqrt{ 2 \frac{ 1 }{ 2 } } \div 3 \sqrt{ 28 }$$

Evaluate

$$\frac{\sqrt{70}}{3}\approx 2.788866755$$

Solution Steps

Multiply 2 and 2 to get 4.

$$\frac{\sqrt{\frac{4+1}{2}}}{3}\sqrt{28}$$

Add 4 and 1 to get 5.

$$\frac{\sqrt{\frac{5}{2}}}{3}\sqrt{28}$$

Rewrite the square root of the division \sqrt{\frac{5}{2}} as the division of square roots \frac{\sqrt{5}}{\sqrt{2}}.

$$\frac{\frac{\sqrt{5}}{\sqrt{2}}}{3}\sqrt{28}$$

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\frac{\sqrt{5}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}}{3}\sqrt{28}$$

The square of \sqrt{2} is 2.

$$\frac{\frac{\sqrt{5}\sqrt{2}}{2}}{3}\sqrt{28}$$

To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\frac{\sqrt{10}}{2}}{3}\sqrt{28}$$

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

$$\frac{\sqrt{10}}{2\times 3}\sqrt{28}$$

Multiply 2 and 3 to get 6.

$$\frac{\sqrt{10}}{6}\sqrt{28}$$

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$\frac{\sqrt{10}}{6}\times 2\sqrt{7}$$

Cancel out 6, the greatest common factor in 2 and 6.

$$\frac{\sqrt{10}}{3}\sqrt{7}$$

Express \frac{\sqrt{10}}{3}\sqrt{7} as a single fraction.

$$\frac{\sqrt{10}\sqrt{7}}{3}$$

To multiply \sqrt{10} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{\sqrt{70}}{3}$$