Solve frac{sqrt{420}}{sqrt{544}}

$$\frac { \sqrt { 420 } } { \sqrt { 544 } }$$

Evaluate

$$\frac{\sqrt{3570}}{68}\approx 0.878668779$$

Solution Steps

Factor 420=2^{2}\times 105. Rewrite the square root of the product \sqrt{2^{2}\times 105} as the product of square roots \sqrt{2^{2}}\sqrt{105}. Take the square root of 2^{2}.

$$\frac{2\sqrt{105}}{\sqrt{544}}$$

Factor 544=4^{2}\times 34. Rewrite the square root of the product \sqrt{4^{2}\times 34} as the product of square roots \sqrt{4^{2}}\sqrt{34}. Take the square root of 4^{2}.

$$\frac{2\sqrt{105}}{4\sqrt{34}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\sqrt{105}}{2\sqrt{34}}$$

Rationalize the denominator of \frac{\sqrt{105}}{2\sqrt{34}} by multiplying numerator and denominator by \sqrt{34}.

$$\frac{\sqrt{105}\sqrt{34}}{2\left(\sqrt{34}\right)^{2}}$$

The square of \sqrt{34} is 34.

$$\frac{\sqrt{105}\sqrt{34}}{2\times 34}$$

To multiply \sqrt{105} and \sqrt{34}, multiply the numbers under the square root.

$$\frac{\sqrt{3570}}{2\times 34}$$

Multiply 2 and 34 to get 68.

$$\frac{\sqrt{3570}}{68}$$