Solve (sqrt{48}-3sqrt{24})divsqrt{6}

$$( \sqrt { 48 } - 3 \sqrt { 24 } ) \div \sqrt { 6 }$$

Evaluate

$$2\sqrt{2}-6\approx -3.171572875$$

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}.

$$\frac{4\sqrt{3}-3\sqrt{24}}{\sqrt{6}}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$\frac{4\sqrt{3}-3\times 2\sqrt{6}}{\sqrt{6}}$$

Multiply -3 and 2 to get -6.

$$\frac{4\sqrt{3}-6\sqrt{6}}{\sqrt{6}}$$

Rationalize the denominator of \frac{4\sqrt{3}-6\sqrt{6}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{\left(4\sqrt{3}-6\sqrt{6}\right)\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{\left(4\sqrt{3}-6\sqrt{6}\right)\sqrt{6}}{6}$$

Use the distributive property to multiply 4\sqrt{3}-6\sqrt{6} by \sqrt{6}.

$$\frac{4\sqrt{3}\sqrt{6}-6\left(\sqrt{6}\right)^{2}}{6}$$

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

$$\frac{4\sqrt{3}\sqrt{3}\sqrt{2}-6\left(\sqrt{6}\right)^{2}}{6}$$

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

$$\frac{4\times 3\sqrt{2}-6\left(\sqrt{6}\right)^{2}}{6}$$

Multiply 4 and 3 to get 12.

$$\frac{12\sqrt{2}-6\left(\sqrt{6}\right)^{2}}{6}$$

The square of \sqrt{6} is 6.

$$\frac{12\sqrt{2}-6\times 6}{6}$$

Multiply -6 and 6 to get -36.

$$\frac{12\sqrt{2}-36}{6}$$