Question

# 15 = 4 + 3w²

$$\displaystyle{15}={4}+{3}{w}²$$

2021-02-05
We are given: $$\displaystyle{15}={4}+{3}{w}²$$
Subtract 4 from both sides: $$\displaystyle{11}={3}{w}²$$
Divide both sides by 3: $$\displaystyle\frac{{11}}{{3}}={w}²$$
Take the square root of both sides:
$$\displaystyle\pm{\left(\sqrt{{\frac{{11}}{{3}}}}\right)}={w}$$
or
$$\displaystyle{w}=\pm\frac{\sqrt{{11}}}{\sqrt{{3}}}$$
Rationalize: $$\displaystyle{w}=\pm{\left(\frac{\sqrt{{11}}}{\sqrt{{3}}}\right)}\cdot{\left(\frac{\sqrt{{3}}}{\sqrt{{3}}}\right)}$$ $$\displaystyle{w}=\pm\frac{\sqrt{{33}}}{{3}}$$