How to solve (sqrt(57/6))+3/2

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve (sqrt(57/6))+3/2 | Equatix

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$$( \sqrt{ 57/6 } )+3/2$$

$\frac{\sqrt{38}+3}{2}\approx 4.582207001$

Reduce the fraction $\frac{57}{6}$ to lowest terms by extracting and canceling out $3$.

$$\sqrt{\frac{19}{2}}+\frac{3}{2}$$

Rewrite the square root of the division $\sqrt{\frac{19}{2}}$ as the division of square roots $\frac{\sqrt{19}}{\sqrt{2}}$.

$$\frac{\sqrt{19}}{\sqrt{2}}+\frac{3}{2}$$

Rationalize the denominator of $\frac{\sqrt{19}}{\sqrt{2}}$ by multiplying numerator and denominator by $\sqrt{2}$.

$$\frac{\sqrt{19}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}+\frac{3}{2}$$

The square of $\sqrt{2}$ is $2$.

$$\frac{\sqrt{19}\sqrt{2}}{2}+\frac{3}{2}$$

To multiply $\sqrt{19}$ and $\sqrt{2}$, multiply the numbers under the square root.

$$\frac{\sqrt{38}}{2}+\frac{3}{2}$$

Since $\frac{\sqrt{38}}{2}$ and $\frac{3}{2}$ have the same denominator, add them by adding their numerators.

$$\frac{\sqrt{38}+3}{2}$$

$\frac{\sqrt{38} + 3}{2} = 4.582207001484488$