Question

Can anyone explain to me how radical equations work? 3 √x + 3 =15

Answer 1

\(\bf 3\sqrt{x}+3=5\quad ?\)

Answer 2

Isolate the square root term to one side and then square it and square everything on the other side 3 sqrt(a) = b
sqrt(a) = b/3
a = (b^2)/9 etc.

Answer 3

\(\bf 3\sqrt{x}+3=5\qquad {\color{red}{ -3}}\\ \quad \\
3\sqrt{x}\cancel{+3-3}=5-3\implies 3\sqrt{x}=2\qquad {\color{red}{ \times \cfrac{1}{3}}}\\ \quad \\
\cfrac{1}{\cancel{3}}\times \cancel{3}\sqrt{x}=2\times \cfrac{1}{3}\implies \sqrt{x}=\cfrac{2}{3}\qquad {\color{red}{ raise\ to\ ^2}}\\ \quad \\
(\sqrt{x})^2=\left(\cfrac{2}{3}\right)^2\implies x=\left(\cfrac{2}{3}\right)^2\)