Solve frac{sqrt{28}*sqrt{147}}{sqrt{189}}

$$\frac { \sqrt { 28 } \times \sqrt { 147 } } { \sqrt { 189 } }$$

Evaluate

$$\frac{14}{3}\approx 4.666666667$$

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}.

$$\frac{2\sqrt{7}\sqrt{147}}{\sqrt{189}}$$

Factor 147=7^{2}\times 3. Rewrite the square root of the product \sqrt{7^{2}\times 3} as the product of square roots \sqrt{7^{2}}\sqrt{3}. Take the square root of 7^{2}.

$$\frac{2\sqrt{7}\times 7\sqrt{3}}{\sqrt{189}}$$

Multiply 2 and 7 to get 14.

$$\frac{14\sqrt{7}\sqrt{3}}{\sqrt{189}}$$

To multiply \sqrt{7} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{14\sqrt{21}}{\sqrt{189}}$$

Factor 189=3^{2}\times 21. Rewrite the square root of the product \sqrt{3^{2}\times 21} as the product of square roots \sqrt{3^{2}}\sqrt{21}. Take the square root of 3^{2}.

$$\frac{14\sqrt{21}}{3\sqrt{21}}$$

Cancel out \sqrt{21} in both numerator and denominator.

$$\frac{14}{3}$$

Factor

$$\frac{2 \cdot 7}{3} = 4\frac{2}{3} = 4.666666666666667$$