Solve frac{sqrt{45}}{2sqrt{20}}=

$$\frac { \sqrt { 45 } } { 2 \sqrt { 20 } } =$$

Evaluate

$$\frac{3}{4}=0.75$$

Solution Steps

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$\frac{3\sqrt{5}}{2\sqrt{20}}$$

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}.

$$\frac{3\sqrt{5}}{2\times 2\sqrt{5}}$$

Multiply 2 and 2 to get 4.

$$\frac{3\sqrt{5}}{4\sqrt{5}}$$

Cancel out \sqrt{5} in both numerator and denominator.

$$\frac{3}{4}$$

Factor

$$\frac{3}{2 ^ {2}} = 0.75$$