Solve frac{sqrt{98*27}}{sqrt{54}}

$$\frac { \sqrt { 98 \cdot 27 } } { \sqrt { 54 } }$$

Evaluate

$$7$$

Solution Steps

Multiply 98 and 27 to get 2646.

$$\frac{\sqrt{2646}}{\sqrt{54}}$$

Factor 2646=21^{2}\times 6. Rewrite the square root of the product \sqrt{21^{2}\times 6} as the product of square roots \sqrt{21^{2}}\sqrt{6}. Take the square root of 21^{2}.

$$\frac{21\sqrt{6}}{\sqrt{54}}$$

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

$$\frac{21\sqrt{6}}{3\sqrt{6}}$$

Cancel out 3\sqrt{6} in both numerator and denominator.

$$7$$

Factor

$$7$$