Solve 3sqrt{75}-sqrt{147}+sqrt{19}

$$3 \sqrt { 75 } - \sqrt { 147 } + \sqrt { 19 }$$

Evaluate

$$\sqrt{19}+8\sqrt{3}\approx 18.215305404$$

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}.

$$3\times 5\sqrt{3}-\sqrt{147}+\sqrt{19}$$

Multiply 3 and 5 to get 15.

$$15\sqrt{3}-\sqrt{147}+\sqrt{19}$$

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}.

$$15\sqrt{3}-7\sqrt{3}+\sqrt{19}$$

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

$$8\sqrt{3}+\sqrt{19}$$