Solve 4sqrt{300}+sqrt{192}+sqrt{243}

$$4 \sqrt { 300 } + \sqrt { 192 } + \sqrt { 243 }$$

Evaluate

$$57\sqrt{3}\approx 98.726896031$$

Solution Steps

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}.

$$4\times 10\sqrt{3}+\sqrt{192}+\sqrt{243}$$

Multiply 4 and 10 to get 40.

$$40\sqrt{3}+\sqrt{192}+\sqrt{243}$$

Factor 192=8^{2}\times 3. Rewrite the square root of the product \sqrt{8^{2}\times 3} as the product of square roots \sqrt{8^{2}}\sqrt{3}. Take the square root of 8^{2}.

$$40\sqrt{3}+8\sqrt{3}+\sqrt{243}$$

Combine 40\sqrt{3} and 8\sqrt{3} to get 48\sqrt{3}.

$$48\sqrt{3}+\sqrt{243}$$

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}.

$$48\sqrt{3}+9\sqrt{3}$$

Combine 48\sqrt{3} and 9\sqrt{3} to get 57\sqrt{3}.

$$57\sqrt{3}$$