Solve 7sqrt{3}-3sqrt{75}+2sqrt{72}-4sqrt{50}

$$7 \sqrt { 3 } - 3 \sqrt { 75 } + 2 \sqrt { 72 } - 4 \sqrt { 50 }$$

Evaluate

$$-8\sqrt{2}-8\sqrt{3}\approx -25.17011496$$

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}.

$$7\sqrt{3}-3\times 5\sqrt{3}+2\sqrt{72}-4\sqrt{50}$$

Multiply -3 and 5 to get -15.

$$7\sqrt{3}-15\sqrt{3}+2\sqrt{72}-4\sqrt{50}$$

Combine 7\sqrt{3} and -15\sqrt{3} to get -8\sqrt{3}.

$$-8\sqrt{3}+2\sqrt{72}-4\sqrt{50}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$-8\sqrt{3}+2\times 6\sqrt{2}-4\sqrt{50}$$

Multiply 2 and 6 to get 12.

$$-8\sqrt{3}+12\sqrt{2}-4\sqrt{50}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$-8\sqrt{3}+12\sqrt{2}-4\times 5\sqrt{2}$$

Multiply -4 and 5 to get -20.

$$-8\sqrt{3}+12\sqrt{2}-20\sqrt{2}$$

Combine 12\sqrt{2} and -20\sqrt{2} to get -8\sqrt{2}.

$$-8\sqrt{3}-8\sqrt{2}$$