Solve (10sqrt{48}-6sqrt{27}+4sqrt{12})divsqrt{3}

$$(10 \sqrt{ 48 } -6 \sqrt{ 27 } +4 \sqrt{ 12 } ) \div \sqrt{ 3 }$$

Evaluate

$$30$$

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}.

$$\frac{10\times 4\sqrt{3}-6\sqrt{27}+4\sqrt{12}}{\sqrt{3}}$$

Multiply 10 and 4 to get 40.

$$\frac{40\sqrt{3}-6\sqrt{27}+4\sqrt{12}}{\sqrt{3}}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$\frac{40\sqrt{3}-6\times 3\sqrt{3}+4\sqrt{12}}{\sqrt{3}}$$

Multiply -6 and 3 to get -18.

$$\frac{40\sqrt{3}-18\sqrt{3}+4\sqrt{12}}{\sqrt{3}}$$

Combine 40\sqrt{3} and -18\sqrt{3} to get 22\sqrt{3}.

$$\frac{22\sqrt{3}+4\sqrt{12}}{\sqrt{3}}$$

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}.

$$\frac{22\sqrt{3}+4\times 2\sqrt{3}}{\sqrt{3}}$$

Multiply 4 and 2 to get 8.

$$\frac{22\sqrt{3}+8\sqrt{3}}{\sqrt{3}}$$

Combine 22\sqrt{3} and 8\sqrt{3} to get 30\sqrt{3}.

$$\frac{30\sqrt{3}}{\sqrt{3}}$$

Rationalize the denominator of \frac{30\sqrt{3}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{30\sqrt{3}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{30\sqrt{3}\sqrt{3}}{3}$$

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

$$\frac{30\times 3}{3}$$

Multiply 30 and 3 to get 90.

$$\frac{90}{3}$$

Divide 90 by 3 to get 30.

$$30$$

Factor

$$2\times 3\times 5$$