Solve sqrt{75}-3sqrt{27}+4sqrt{48}-10sqrt{3}

$$\sqrt { 75 } - 3 \sqrt { 27 } + 4 \sqrt { 48 } - 10 \sqrt { 3 }$$

Evaluate

$$2\sqrt{3}\approx 3.464101615$$

Solution Steps

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}.

$$5\sqrt{3}-3\sqrt{27}+4\sqrt{48}-10\sqrt{3}$$

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}.

$$5\sqrt{3}-3\times 3\sqrt{3}+4\sqrt{48}-10\sqrt{3}$$

Multiply -3 and 3 to get -9.

$$5\sqrt{3}-9\sqrt{3}+4\sqrt{48}-10\sqrt{3}$$

Combine 5\sqrt{3} and -9\sqrt{3} to get -4\sqrt{3}.

$$-4\sqrt{3}+4\sqrt{48}-10\sqrt{3}$$

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}.

$$-4\sqrt{3}+4\times 4\sqrt{3}-10\sqrt{3}$$

Multiply 4 and 4 to get 16.

$$-4\sqrt{3}+16\sqrt{3}-10\sqrt{3}$$

Combine -4\sqrt{3} and 16\sqrt{3} to get 12\sqrt{3}.

$$12\sqrt{3}-10\sqrt{3}$$

Combine 12\sqrt{3} and -10\sqrt{3} to get 2\sqrt{3}.

$$2\sqrt{3}$$