Solve frac{16sqrt{20}}{2sqrt{2}}=

$$\frac { 16 \sqrt { 20 } } { 2 \sqrt { 2 } } =$$

Evaluate

$$8\sqrt{10}\approx 25.298221281$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{8\sqrt{20}}{\sqrt{2}}$$

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\frac{8\times 2\sqrt{5}}{\sqrt{2}}$$

Multiply 8 and 2 to get 16.

$$\frac{16\sqrt{5}}{\sqrt{2}}$$

Rationalize the denominator of \frac{16\sqrt{5}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{16\sqrt{5}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{16\sqrt{5}\sqrt{2}}{2}$$

To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{16\sqrt{10}}{2}$$

Divide 16\sqrt{10} by 2 to get 8\sqrt{10}.

$$8\sqrt{10}$$