Solve frac{37+sqrt{54}}{(1-4)^2}

$$\frac { 37 + \sqrt { 54 } } { ( 1 - 4 ) ^ { 2 } }$$

Evaluate

$$\frac{\sqrt{6}}{3}+\frac{37}{9}\approx 4.927607692$$

Solution Steps

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

$$\frac{37+3\sqrt{6}}{\left(1-4\right)^{2}}$$

Subtract 4 from 1 to get -3.

$$\frac{37+3\sqrt{6}}{\left(-3\right)^{2}}$$

Calculate -3 to the power of 2 and get 9.

$$\frac{37+3\sqrt{6}}{9}$$