Solve 7sqrt{108}-4sqrt{18}-sqrt{3}

$$7 \sqrt { 108 } - 4 \sqrt { 18 } - \sqrt { 3 }$$

Evaluate

$$41\sqrt{3}-12\sqrt{2}\approx 54.043520362$$

Solution Steps

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}.

$$7\times 6\sqrt{3}-4\sqrt{18}-\sqrt{3}$$

Multiply 7 and 6 to get 42.

$$42\sqrt{3}-4\sqrt{18}-\sqrt{3}$$

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}.

$$42\sqrt{3}-4\times 3\sqrt{2}-\sqrt{3}$$

Multiply -4 and 3 to get -12.

$$42\sqrt{3}-12\sqrt{2}-\sqrt{3}$$

Combine 42\sqrt{3} and -\sqrt{3} to get 41\sqrt{3}.

$$41\sqrt{3}-12\sqrt{2}$$