Solve -7sqrt{8}div1/sqrt{2}

$$- 7 \sqrt { 8 } \div \frac { 1 } { \sqrt { 2 } }$$

Evaluate

$$-28$$

Solution Steps

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}.

$$\frac{-7\times 2\sqrt{2}}{\frac{1}{\sqrt{2}}}$$

Multiply -7 and 2 to get -14.

$$\frac{-14\sqrt{2}}{\frac{1}{\sqrt{2}}}$$

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

$$\frac{-14\sqrt{2}}{\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}}$$

The square of \sqrt{2} is 2.

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

Divide -14\sqrt{2} by \frac{\sqrt{2}}{2} by multiplying -14\sqrt{2} by the reciprocal of \frac{\sqrt{2}}{2}.

$$\frac{-14\sqrt{2}\times 2}{\sqrt{2}}$$

Rationalize the denominator of \frac{-14\sqrt{2}\times 2}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{-14\sqrt{2}\times 2\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{-14\sqrt{2}\times 2\sqrt{2}}{2}$$

Multiply -14 and 2 to get -28.

$$\frac{-28\sqrt{2}\sqrt{2}}{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{-28\times 2}{2}$$

Multiply -28 and 2 to get -56.

$$\frac{-56}{2}$$

Divide -56 by 2 to get -28.

$$-28$$

Factor

$$-28$$