Solve 5sqrt{2}-2sqrt{108}-7sqrt{3}+9sqrt{2}

$$5 \sqrt{ 2 } -2 \sqrt{ 108 } -7 \sqrt{ 3 } +9 \sqrt{ 2 }$$

Evaluate

$$14\sqrt{2}-19\sqrt{3}\approx -13.109975471$$

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}.

$$5\sqrt{2}-2\times 6\sqrt{3}-7\sqrt{3}+9\sqrt{2}$$

Multiply -2 and 6 to get -12.

$$5\sqrt{2}-12\sqrt{3}-7\sqrt{3}+9\sqrt{2}$$

Combine -12\sqrt{3} and -7\sqrt{3} to get -19\sqrt{3}.

$$5\sqrt{2}-19\sqrt{3}+9\sqrt{2}$$

Combine 5\sqrt{2} and 9\sqrt{2} to get 14\sqrt{2}.

$$14\sqrt{2}-19\sqrt{3}$$