Solve 3*sqrt{48}-sqrt{300}

$$3 \cdot \sqrt { 48 } - \sqrt { 300 }$$

Evaluate

$$2\sqrt{3}\approx 3.464101615$$

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}.

$$3\times 4\sqrt{3}-\sqrt{300}$$

Multiply 3 and 4 to get 12.

$$12\sqrt{3}-\sqrt{300}$$

Factor 300=10^{2}\times 3. Rewrite the square root of the product \sqrt{10^{2}\times 3} as the product of square roots \sqrt{10^{2}}\sqrt{3}. Take the square root of 10^{2}.

$$12\sqrt{3}-10\sqrt{3}$$

Combine 12\sqrt{3} and -10\sqrt{3} to get 2\sqrt{3}.

$$2\sqrt{3}$$