Solve 8sqrt{27}-6sqrt{147}+3sqrt{75}-2sqrt{48}

$$8 \sqrt{ 27 } -6 \sqrt{ 147 } +3 \sqrt{ 75 } -2 \sqrt{ 48 }$$

Evaluate

$$-11\sqrt{3}\approx -19.052558883$$

Solution Steps

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}.

$$8\times 3\sqrt{3}-6\sqrt{147}+3\sqrt{75}-2\sqrt{48}$$

Multiply 8 and 3 to get 24.

$$24\sqrt{3}-6\sqrt{147}+3\sqrt{75}-2\sqrt{48}$$

Factor 147=7^{2}\times 3. Rewrite the square root of the product \sqrt{7^{2}\times 3} as the product of square roots \sqrt{7^{2}}\sqrt{3}. Take the square root of 7^{2}.

$$24\sqrt{3}-6\times 7\sqrt{3}+3\sqrt{75}-2\sqrt{48}$$

Multiply -6 and 7 to get -42.

$$24\sqrt{3}-42\sqrt{3}+3\sqrt{75}-2\sqrt{48}$$

Combine 24\sqrt{3} and -42\sqrt{3} to get -18\sqrt{3}.

$$-18\sqrt{3}+3\sqrt{75}-2\sqrt{48}$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$-18\sqrt{3}+3\times 5\sqrt{3}-2\sqrt{48}$$

Multiply 3 and 5 to get 15.

$$-18\sqrt{3}+15\sqrt{3}-2\sqrt{48}$$

Combine -18\sqrt{3} and 15\sqrt{3} to get -3\sqrt{3}.

$$-3\sqrt{3}-2\sqrt{48}$$

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}.

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

Multiply -2 and 4 to get -8.

$$-3\sqrt{3}-8\sqrt{3}$$

Combine -3\sqrt{3} and -8\sqrt{3} to get -11\sqrt{3}.

$$-11\sqrt{3}$$