Solve 1622/45%sqrt{32}

$$\frac{ 1622 }{ 45 \% \sqrt{ 32 } }$$

Evaluate

$$\frac{4055\sqrt{2}}{9}\approx 637.181777269$$

Solution Steps

Reduce the fraction \frac{45}{100} to lowest terms by extracting and canceling out 5.

$$\frac{1622}{\frac{9}{20}\sqrt{32}}$$

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}.

$$\frac{1622}{\frac{9}{20}\times 4\sqrt{2}}$$

Express \frac{9}{20}\times 4 as a single fraction.

$$\frac{1622}{\frac{9\times 4}{20}\sqrt{2}}$$

Multiply 9 and 4 to get 36.

$$\frac{1622}{\frac{36}{20}\sqrt{2}}$$

Reduce the fraction \frac{36}{20} to lowest terms by extracting and canceling out 4.

$$\frac{1622}{\frac{9}{5}\sqrt{2}}$$

Rationalize the denominator of \frac{1622}{\frac{9}{5}\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{1622\sqrt{2}}{\frac{9}{5}\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{1622\sqrt{2}}{\frac{9}{5}\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{811\sqrt{2}}{\frac{9}{5}}$$

Divide 811\sqrt{2} by \frac{9}{5} by multiplying 811\sqrt{2} by the reciprocal of \frac{9}{5}.

$$\frac{811\sqrt{2}\times 5}{9}$$

Multiply 811 and 5 to get 4055.

$$\frac{4055\sqrt{2}}{9}$$