Solve sqrt{48}-4sqrt{75}+2sqrt{243}

$$\sqrt{ 48 } -4 \sqrt{ 75 } +2 \sqrt{ 243 }$$

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}.

$$4\sqrt{3}-4\sqrt{75}+2\sqrt{243}$$

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}.

$$4\sqrt{3}-4\times 5\sqrt{3}+2\sqrt{243}$$

Multiply -4 and 5 to get -20.

$$4\sqrt{3}-20\sqrt{3}+2\sqrt{243}$$

Combine 4\sqrt{3} and -20\sqrt{3} to get -16\sqrt{3}.

$$-16\sqrt{3}+2\sqrt{243}$$

Factor 243=9^{2}\times 3. Rewrite the square root of the product \sqrt{9^{2}\times 3} as the product of square roots \sqrt{9^{2}}\sqrt{3}. Take the square root of 9^{2}.

$$-16\sqrt{3}+2\times 9\sqrt{3}$$

Multiply 2 and 9 to get 18.

$$-16\sqrt{3}+18\sqrt{3}$$

Combine -16\sqrt{3} and 18\sqrt{3} to get 2\sqrt{3}.

$$2\sqrt{3}$$