Solve frac{sqrt{90}}{sqrt{40}}

$$\frac { \sqrt { 90 } } { \sqrt { 40 } }$$

Evaluate

$$\frac{3}{2}=1.5$$

Solution Steps

Factor 90=3^{2}\times 10. Rewrite the square root of the product \sqrt{3^{2}\times 10} as the product of square roots \sqrt{3^{2}}\sqrt{10}. Take the square root of 3^{2}.

$$\frac{3\sqrt{10}}{\sqrt{40}}$$

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$\frac{3\sqrt{10}}{2\sqrt{10}}$$

Cancel out \sqrt{10} in both numerator and denominator.

$$\frac{3}{2}$$

Factor

$$\frac{3}{2} = 1\frac{1}{2} = 1.5$$