Solve sqrt{20}divsqrt{28}

$$\sqrt{ 20 } \div \sqrt{ 28 }$$

Evaluate

$$\frac{\sqrt{35}}{7}\approx 0.845154255$$

Solution Steps

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}.

$$\frac{2\sqrt{5}}{\sqrt{28}}$$

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$\frac{2\sqrt{5}}{2\sqrt{7}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\sqrt{5}}{\sqrt{7}}$$

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{\sqrt{5}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{\sqrt{5}\sqrt{7}}{7}$$

To multiply \sqrt{5} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{\sqrt{35}}{7}$$