Solve sqrt{48}+sqrt{48}+sqrt{363}+sqrt{363}

$$\sqrt{ 48 } + \sqrt{ 48 } + \sqrt{ 363 } + \sqrt{ 363 }$$

Evaluate

$$30\sqrt{3}\approx 51.961524227$$

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}.

$$4\sqrt{3}+\sqrt{48}+\sqrt{363}+\sqrt{363}$$

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}.

$$4\sqrt{3}+4\sqrt{3}+\sqrt{363}+\sqrt{363}$$

Combine 4\sqrt{3} and 4\sqrt{3} to get 8\sqrt{3}.

$$8\sqrt{3}+\sqrt{363}+\sqrt{363}$$

Factor 363=11^{2}\times 3. Rewrite the square root of the product \sqrt{11^{2}\times 3} as the product of square roots \sqrt{11^{2}}\sqrt{3}. Take the square root of 11^{2}.

$$8\sqrt{3}+11\sqrt{3}+\sqrt{363}$$

Combine 8\sqrt{3} and 11\sqrt{3} to get 19\sqrt{3}.

$$19\sqrt{3}+\sqrt{363}$$

Factor 363=11^{2}\times 3. Rewrite the square root of the product \sqrt{11^{2}\times 3} as the product of square roots \sqrt{11^{2}}\sqrt{3}. Take the square root of 11^{2}.

$$19\sqrt{3}+11\sqrt{3}$$

Combine 19\sqrt{3} and 11\sqrt{3} to get 30\sqrt{3}.

$$30\sqrt{3}$$