Solve frac{sqrt{15}*sqrt{105}}{sqrt{18}*sqrt{14}}

$$\frac { \sqrt { 15 } \cdot \sqrt { 105 } } { \sqrt { 18 } \cdot \sqrt { 14 } }$$

Evaluate

$$\frac{5}{2}=2.5$$

Solution Steps

Factor 105=15\times 7. Rewrite the square root of the product \sqrt{15\times 7} as the product of square roots \sqrt{15}\sqrt{7}.

$$\frac{\sqrt{15}\sqrt{15}\sqrt{7}}{\sqrt{18}\sqrt{14}}$$

Multiply \sqrt{15} and \sqrt{15} to get 15.

$$\frac{15\sqrt{7}}{\sqrt{18}\sqrt{14}}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$\frac{15\sqrt{7}}{3\sqrt{2}\sqrt{14}}$$

Factor 14=2\times 7. Rewrite the square root of the product \sqrt{2\times 7} as the product of square roots \sqrt{2}\sqrt{7}.

$$\frac{15\sqrt{7}}{3\sqrt{2}\sqrt{2}\sqrt{7}}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$\frac{15\sqrt{7}}{3\times 2\sqrt{7}}$$

Cancel out 3\sqrt{7} in both numerator and denominator.

$$\frac{5}{2}$$

Factor

$$\frac{5}{2} = 2\frac{1}{2} = 2.5$$