Solve sqrt{147}-4sqrt{108}+sqrt{75}

$$\sqrt{ 147 } -4 \sqrt{ 108 } + \sqrt{ 75 }$$

Evaluate

$$-12\sqrt{3}\approx -20.784609691$$

Solution Steps

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}.

$$7\sqrt{3}-4\sqrt{108}+\sqrt{75}$$

Factor 108=6^{2}\times 3. Rewrite the square root of the product \sqrt{6^{2}\times 3} as the product of square roots \sqrt{6^{2}}\sqrt{3}. Take the square root of 6^{2}.

$$7\sqrt{3}-4\times 6\sqrt{3}+\sqrt{75}$$

Multiply -4 and 6 to get -24.

$$7\sqrt{3}-24\sqrt{3}+\sqrt{75}$$

Combine 7\sqrt{3} and -24\sqrt{3} to get -17\sqrt{3}.

$$-17\sqrt{3}+\sqrt{75}$$

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}.

$$-17\sqrt{3}+5\sqrt{3}$$

Combine -17\sqrt{3} and 5\sqrt{3} to get -12\sqrt{3}.

$$-12\sqrt{3}$$