Solve 4sqrt{28}:3sqrt{7}

$$4 \sqrt { 28 } : 3 \sqrt { 7 }$$

Evaluate

$$\frac{56}{3}\approx 18.666666667$$

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}.

$$\frac{4\times 2\sqrt{7}}{3}\sqrt{7}$$

Multiply 4 and 2 to get 8.

$$\frac{8\sqrt{7}}{3}\sqrt{7}$$

Express \frac{8\sqrt{7}}{3}\sqrt{7} as a single fraction.

$$\frac{8\sqrt{7}\sqrt{7}}{3}$$

Multiply \sqrt{7} and \sqrt{7} to get 7.

$$\frac{8\times 7}{3}$$

Multiply 8 and 7 to get 56.

$$\frac{56}{3}$$

Factor

$$\frac{2 ^ {3} \cdot 7}{3} = 18\frac{2}{3} = 18.666666666666668$$