Solve frac{6sqrt{28}}{sqrt{63}}=

$$\frac { 6 \sqrt { 28 } } { \sqrt { 63 } } =$$

Evaluate

$$4$$

Solution Steps

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$\frac{6\times 2\sqrt{7}}{\sqrt{63}}$$

Multiply 6 and 2 to get 12.

$$\frac{12\sqrt{7}}{\sqrt{63}}$$

Factor 63=3^{2}\times 7. Rewrite the square root of the product \sqrt{3^{2}\times 7} as the product of square roots \sqrt{3^{2}}\sqrt{7}. Take the square root of 3^{2}.

$$\frac{12\sqrt{7}}{3\sqrt{7}}$$

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

$$4$$

Factor

$$2^{2}$$