Solve (sqrt{72}-sqrt{8})divsqrt{2}=

$$( \sqrt { 72 } - \sqrt { 8 } ) \div \sqrt { 2 } =$$

Evaluate

$$4$$

Solution Steps

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$\frac{6\sqrt{2}-\sqrt{8}}{\sqrt{2}}$$

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}.

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

Combine 6\sqrt{2} and -2\sqrt{2} to get 4\sqrt{2}.

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

Rationalize the denominator of \frac{4\sqrt{2}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{4\sqrt{2}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

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

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

$$\frac{4\times 2}{2}$$

Multiply 4 and 2 to get 8.

$$\frac{8}{2}$$

Divide 8 by 2 to get 4.

$$4$$

Factor

$$2^{2}$$