Solve 3sqrt{48}*sqrt{5}divsqrt{12}

$$3 \sqrt{ 48 } \times \sqrt{ 5 } \div \sqrt{ 12 }$$

Evaluate

$$6\sqrt{5}\approx 13.416407865$$

Solution Steps

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$\frac{3\times 4\sqrt{3}\sqrt{5}}{\sqrt{12}}$$

Multiply 3 and 4 to get 12.

$$\frac{12\sqrt{3}\sqrt{5}}{\sqrt{12}}$$

To multiply \sqrt{3} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{12\sqrt{15}}{\sqrt{12}}$$

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}.

$$\frac{12\sqrt{15}}{2\sqrt{3}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{6\sqrt{15}}{\sqrt{3}}$$

Rationalize the denominator of \frac{6\sqrt{15}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{6\sqrt{15}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{6\sqrt{15}\sqrt{3}}{3}$$

Factor 15=3\times 5. Rewrite the square root of the product \sqrt{3\times 5} as the product of square roots \sqrt{3}\sqrt{5}.

$$\frac{6\sqrt{3}\sqrt{5}\sqrt{3}}{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{6\times 3\sqrt{5}}{3}$$

Cancel out 3 and 3.

$$6\sqrt{5}$$