Solve 3sqrt{12}-sqrt{48}+sqrt{30,000}

$$3 \sqrt { 12 } - \sqrt { 48 } + \sqrt { 30,000 }$$

Evaluate

$$102\sqrt{3}\approx 176.669182372$$

Solution Steps

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}.

$$3\times 2\sqrt{3}-\sqrt{48}+\sqrt{30000}$$

Multiply 3 and 2 to get 6.

$$6\sqrt{3}-\sqrt{48}+\sqrt{30000}$$

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}.

$$6\sqrt{3}-4\sqrt{3}+\sqrt{30000}$$

Combine 6\sqrt{3} and -4\sqrt{3} to get 2\sqrt{3}.

$$2\sqrt{3}+\sqrt{30000}$$

Factor 30000=100^{2}\times 3. Rewrite the square root of the product \sqrt{100^{2}\times 3} as the product of square roots \sqrt{100^{2}}\sqrt{3}. Take the square root of 100^{2}.

$$2\sqrt{3}+100\sqrt{3}$$

Combine 2\sqrt{3} and 100\sqrt{3} to get 102\sqrt{3}.

$$102\sqrt{3}$$