Solve (-7sqrt{1/28})(-1/3sqrt{126})

$$( - 7 \sqrt { \frac { 1 } { 28 } } ) ( - \frac { 1 } { 3 } \sqrt { 126 } )$$

Evaluate

$$\frac{7\sqrt{2}}{2}\approx 4.949747468$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{28}} as the division of square roots \frac{\sqrt{1}}{\sqrt{28}}.

$$-7\times \frac{\sqrt{1}}{\sqrt{28}}\left(-\frac{1}{3}\right)\sqrt{126}$$

Calculate the square root of 1 and get 1.

$$-7\times \frac{1}{\sqrt{28}}\left(-\frac{1}{3}\right)\sqrt{126}$$

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}.

$$-7\times \frac{1}{2\sqrt{7}}\left(-\frac{1}{3}\right)\sqrt{126}$$

Rationalize the denominator of \frac{1}{2\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$-7\times \frac{\sqrt{7}}{2\left(\sqrt{7}\right)^{2}}\left(-\frac{1}{3}\right)\sqrt{126}$$

The square of \sqrt{7} is 7.

$$-7\times \frac{\sqrt{7}}{2\times 7}\left(-\frac{1}{3}\right)\sqrt{126}$$

Multiply 2 and 7 to get 14.

$$-7\times \frac{\sqrt{7}}{14}\left(-\frac{1}{3}\right)\sqrt{126}$$

Express -7\left(-\frac{1}{3}\right) as a single fraction.

$$\frac{-7\left(-1\right)}{3}\times \frac{\sqrt{7}}{14}\sqrt{126}$$

Multiply -7 and -1 to get 7.

$$\frac{7}{3}\times \frac{\sqrt{7}}{14}\sqrt{126}$$

Factor 126=3^{2}\times 14. Rewrite the square root of the product \sqrt{3^{2}\times 14} as the product of square roots \sqrt{3^{2}}\sqrt{14}. Take the square root of 3^{2}.

$$\frac{7}{3}\times \frac{\sqrt{7}}{14}\times 3\sqrt{14}$$

Cancel out 3 and 3.

$$7\times \frac{\sqrt{7}}{14}\sqrt{14}$$

Cancel out 14, the greatest common factor in 7 and 14.

$$\frac{\sqrt{7}}{2}\sqrt{14}$$

Express \frac{\sqrt{7}}{2}\sqrt{14} as a single fraction.

$$\frac{\sqrt{7}\sqrt{14}}{2}$$

Factor 14=7\times 2. Rewrite the square root of the product \sqrt{7\times 2} as the product of square roots \sqrt{7}\sqrt{2}.

$$\frac{\sqrt{7}\sqrt{7}\sqrt{2}}{2}$$

Multiply \sqrt{7} and \sqrt{7} to get 7.

$$\frac{7\sqrt{2}}{2}$$