Solve 64/sqrt{32}-14/sqrt{2}

$$\frac { 64 } { \sqrt { 32 } } - \frac { 14 } { \sqrt { 2 } }$$

Evaluate

$$\sqrt{2}\approx 1.414213562$$

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}.

$$\frac{64}{4\sqrt{2}}-\frac{14}{\sqrt{2}}$$

Rationalize the denominator of \frac{64}{4\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{64\sqrt{2}}{4\left(\sqrt{2}\right)^{2}}-\frac{14}{\sqrt{2}}$$

The square of \sqrt{2} is 2.

$$\frac{64\sqrt{2}}{4\times 2}-\frac{14}{\sqrt{2}}$$

Cancel out 2\times 4 in both numerator and denominator.

$$8\sqrt{2}-\frac{14}{\sqrt{2}}$$

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

$$8\sqrt{2}-\frac{14\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$8\sqrt{2}-\frac{14\sqrt{2}}{2}$$

Divide 14\sqrt{2} by 2 to get 7\sqrt{2}.

$$8\sqrt{2}-7\sqrt{2}$$

Combine 8\sqrt{2} and -7\sqrt{2} to get \sqrt{2}.

$$\sqrt{2}$$