Solve 2sqrt{12}+5sqrt{48}-sqrt{75}

$$2 \sqrt { 12 } + 5 \sqrt { 48 } - \sqrt { 75 }$$

Evaluate

$$19\sqrt{3}\approx 32.908965344$$

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}.

$$2\times 2\sqrt{3}+5\sqrt{48}-\sqrt{75}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{3}+5\sqrt{48}-\sqrt{75}$$

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}.

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

Multiply 5 and 4 to get 20.

$$4\sqrt{3}+20\sqrt{3}-\sqrt{75}$$

Combine 4\sqrt{3} and 20\sqrt{3} to get 24\sqrt{3}.

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

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}.

$$24\sqrt{3}-5\sqrt{3}$$

Combine 24\sqrt{3} and -5\sqrt{3} to get 19\sqrt{3}.

$$19\sqrt{3}$$