Solve 10sqrt{3}-7sqrt{75}+2sqrt{243}

$$10 \sqrt{ 3 } -7 \sqrt{ 75 } +2 \sqrt{ 243 }$$

Evaluate

$$-7\sqrt{3}\approx -12.124355653$$

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}.

$$10\sqrt{3}-7\times 5\sqrt{3}+2\sqrt{243}$$

Multiply -7 and 5 to get -35.

$$10\sqrt{3}-35\sqrt{3}+2\sqrt{243}$$

Combine 10\sqrt{3} and -35\sqrt{3} to get -25\sqrt{3}.

$$-25\sqrt{3}+2\sqrt{243}$$

Factor 243=9^{2}\times 3. Rewrite the square root of the product \sqrt{9^{2}\times 3} as the product of square roots \sqrt{9^{2}}\sqrt{3}. Take the square root of 9^{2}.

$$-25\sqrt{3}+2\times 9\sqrt{3}$$

Multiply 2 and 9 to get 18.

$$-25\sqrt{3}+18\sqrt{3}$$

Combine -25\sqrt{3} and 18\sqrt{3} to get -7\sqrt{3}.

$$-7\sqrt{3}$$