Solve sqrt{48}+5sqrt{12}-sqrt{147}+sqrt{75}

$$\sqrt{ 48 } +5 \sqrt{ 12 } - \sqrt{ 147 } + \sqrt{ 75 }$$

Evaluate

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

Solution Steps

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}.

$$4\sqrt{3}+5\sqrt{12}-\sqrt{147}+\sqrt{75}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$4\sqrt{3}+5\times 2\sqrt{3}-\sqrt{147}+\sqrt{75}$$

Multiply 5 and 2 to get 10.

$$4\sqrt{3}+10\sqrt{3}-\sqrt{147}+\sqrt{75}$$

Combine 4\sqrt{3} and 10\sqrt{3} to get 14\sqrt{3}.

$$14\sqrt{3}-\sqrt{147}+\sqrt{75}$$

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}.

$$14\sqrt{3}-7\sqrt{3}+\sqrt{75}$$

Combine 14\sqrt{3} and -7\sqrt{3} to get 7\sqrt{3}.

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

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}.

$$7\sqrt{3}+5\sqrt{3}$$

Combine 7\sqrt{3} and 5\sqrt{3} to get 12\sqrt{3}.

$$12\sqrt{3}$$