Solve (4sqrt{32}-6sqrt{18})divsqrt{2}

$$( 4 \sqrt { 32 } - 6 \sqrt { 18 } ) \div \sqrt { 2 }$$

Evaluate

$$-2$$

Solution Steps

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$\frac{4\times 4\sqrt{2}-6\sqrt{18}}{\sqrt{2}}$$

Multiply 4 and 4 to get 16.

$$\frac{16\sqrt{2}-6\sqrt{18}}{\sqrt{2}}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$\frac{16\sqrt{2}-6\times 3\sqrt{2}}{\sqrt{2}}$$

Multiply -6 and 3 to get -18.

$$\frac{16\sqrt{2}-18\sqrt{2}}{\sqrt{2}}$$

Combine 16\sqrt{2} and -18\sqrt{2} to get -2\sqrt{2}.

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

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

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

The square of \sqrt{2} is 2.

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

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

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

Multiply -2 and 2 to get -4.

$$\frac{-4}{2}$$

Divide -4 by 2 to get -2.

$$-2$$

Factor

$$-2$$