Solve 4sqrt{18}-6sqrt{2}+1+9sqrt{3}-sqrt{75}=

$$4 \sqrt { 18 } - 6 \sqrt { 2 } + 1 + 9 \sqrt { 3 } - \sqrt { 75 } =$$

Evaluate

$$4\sqrt{3}+6\sqrt{2}+1\approx 16.413484605$$

Solution Steps

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$4\times 3\sqrt{2}-6\sqrt{2}+1+9\sqrt{3}-\sqrt{75}$$

Multiply 4 and 3 to get 12.

$$12\sqrt{2}-6\sqrt{2}+1+9\sqrt{3}-\sqrt{75}$$

Combine 12\sqrt{2} and -6\sqrt{2} to get 6\sqrt{2}.

$$6\sqrt{2}+1+9\sqrt{3}-\sqrt{75}$$

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}.

$$6\sqrt{2}+1+9\sqrt{3}-5\sqrt{3}$$

Combine 9\sqrt{3} and -5\sqrt{3} to get 4\sqrt{3}.

$$6\sqrt{2}+1+4\sqrt{3}$$