Solve 5sqrt{50}+3sqrt{108}-10sqrt{2}+4sqrt{12}

$$5 \sqrt{ 50 } +3 \sqrt{ 108 } -10 \sqrt{ 2 } +4 \sqrt{ 12 }$$

Evaluate

$$15\sqrt{2}+26\sqrt{3}\approx 66.246524432$$

Solution Steps

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$5\times 5\sqrt{2}+3\sqrt{108}-10\sqrt{2}+4\sqrt{12}$$

Multiply 5 and 5 to get 25.

$$25\sqrt{2}+3\sqrt{108}-10\sqrt{2}+4\sqrt{12}$$

Factor 108=6^{2}\times 3. Rewrite the square root of the product \sqrt{6^{2}\times 3} as the product of square roots \sqrt{6^{2}}\sqrt{3}. Take the square root of 6^{2}.

$$25\sqrt{2}+3\times 6\sqrt{3}-10\sqrt{2}+4\sqrt{12}$$

Multiply 3 and 6 to get 18.

$$25\sqrt{2}+18\sqrt{3}-10\sqrt{2}+4\sqrt{12}$$

Combine 25\sqrt{2} and -10\sqrt{2} to get 15\sqrt{2}.

$$15\sqrt{2}+18\sqrt{3}+4\sqrt{12}$$

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}.

$$15\sqrt{2}+18\sqrt{3}+4\times 2\sqrt{3}$$

Multiply 4 and 2 to get 8.

$$15\sqrt{2}+18\sqrt{3}+8\sqrt{3}$$

Combine 18\sqrt{3} and 8\sqrt{3} to get 26\sqrt{3}.

$$15\sqrt{2}+26\sqrt{3}$$