Solve 3sqrt{92}-6sqrt{18}

$$3 \sqrt{ 92 } -6 \sqrt{ 18 }$$

Evaluate

$$6\left(\sqrt{23}-3\sqrt{2}\right)\approx 3.319145017$$

Solution Steps

Factor 92=2^{2}\times 23. Rewrite the square root of the product \sqrt{2^{2}\times 23} as the product of square roots \sqrt{2^{2}}\sqrt{23}. Take the square root of 2^{2}.

$$3\times 2\sqrt{23}-6\sqrt{18}$$

Multiply 3 and 2 to get 6.

$$6\sqrt{23}-6\sqrt{18}$$

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}.

$$6\sqrt{23}-6\times 3\sqrt{2}$$

Multiply -6 and 3 to get -18.

$$6\sqrt{23}-18\sqrt{2}$$

Factor

$$6 {(\sqrt{23} - 3 \sqrt{2})} = 3.319145017$$