Solve 4sqrt{25}*sqrt{12}:sqrt{72}

$$4 \sqrt { 25 } \times \sqrt { 12 } : \sqrt { 72 }$$

Evaluate

$$\frac{10\sqrt{6}}{3}\approx 8.164965809$$

Solution Steps

Calculate the square root of 25 and get 5.

$$\frac{4\times 5\sqrt{12}}{\sqrt{72}}$$

Multiply 4 and 5 to get 20.

$$\frac{20\sqrt{12}}{\sqrt{72}}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{20\times 2\sqrt{3}}{\sqrt{72}}$$

Multiply 20 and 2 to get 40.

$$\frac{40\sqrt{3}}{\sqrt{72}}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$\frac{40\sqrt{3}}{6\sqrt{2}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{20\sqrt{3}}{3\sqrt{2}}$$

Rationalize the denominator of \frac{20\sqrt{3}}{3\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{20\sqrt{3}\sqrt{2}}{3\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{20\sqrt{3}\sqrt{2}}{3\times 2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{20\sqrt{6}}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$\frac{20\sqrt{6}}{6}$$

Divide 20\sqrt{6} by 6 to get \frac{10}{3}\sqrt{6}.

$$\frac{10}{3}\sqrt{6}$$