Solve frac{sqrt{5+2}}{3}x^2-3

$$\frac { \sqrt { 5 + 2 } } { 3 } x ^ { 2 } - 3$$

Evaluate

$$\frac{\sqrt{7}x^{2}}{3}-3$$

Short Solution Steps

Add 5 and 2 to get 7.

$$\frac{\sqrt{7}}{3}x^{2}-3$$

Express \frac{\sqrt{7}}{3}x^{2} as a single fraction.

$$\frac{\sqrt{7}x^{2}}{3}-3$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{3}{3}.

$$\frac{\sqrt{7}x^{2}}{3}-\frac{3\times 3}{3}$$

Since \frac{\sqrt{7}x^{2}}{3} and \frac{3\times 3}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\sqrt{7}x^{2}-3\times 3}{3}$$

Do the multiplications in \sqrt{7}x^{2}-3\times 3.

$$\frac{\sqrt{7}x^{2}-9}{3}$$

Factor

$$\frac{\sqrt{7}x^{2}-9}{3}$$

Solution Steps

Factor out \frac{1}{3}. Polynomial \sqrt{7}x^{2}-9 is not factored since it does not have any rational roots.

$$\frac{\sqrt{7}x^{2}-9}{3}$$