Solve 3/25*sqrt{32}=

$$\frac{ 3 }{ 25 \times \sqrt{ 32 } } =$$

Evaluate

$$\frac{3\sqrt{2}}{200}\approx 0.021213203$$

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}.

$$\frac{3}{25\times 4\sqrt{2}}$$

Multiply 25 and 4 to get 100.

$$\frac{3}{100\sqrt{2}}$$

Rationalize the denominator of \frac{3}{100\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{3\sqrt{2}}{100\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{3\sqrt{2}}{100\times 2}$$

Multiply 100 and 2 to get 200.

$$\frac{3\sqrt{2}}{200}$$