Solve 2sqrt{2(32)/1.75}

$$2 \sqrt{ \frac{ 2(32) }{ 1.75 } }$$

Evaluate

$$\frac{32\sqrt{7}}{7}\approx 12.094863136$$

Solution Steps

Multiply 2 and 32 to get 64.

$$2\sqrt{\frac{64}{1.75}}$$

Expand \frac{64}{1.75} by multiplying both numerator and the denominator by 100.

$$2\sqrt{\frac{6400}{175}}$$

Reduce the fraction \frac{6400}{175} to lowest terms by extracting and canceling out 25.

$$2\sqrt{\frac{256}{7}}$$

Rewrite the square root of the division \sqrt{\frac{256}{7}} as the division of square roots \frac{\sqrt{256}}{\sqrt{7}}.

$$2\times \frac{\sqrt{256}}{\sqrt{7}}$$

Calculate the square root of 256 and get 16.

$$2\times \frac{16}{\sqrt{7}}$$

Rationalize the denominator of \frac{16}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$2\times \frac{16\sqrt{7}}{\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$2\times \frac{16\sqrt{7}}{7}$$

Express 2\times \frac{16\sqrt{7}}{7} as a single fraction.

$$\frac{2\times 16\sqrt{7}}{7}$$

Multiply 2 and 16 to get 32.

$$\frac{32\sqrt{7}}{7}$$