Question

How do you solve `sqrt (x+9)=4`?

Answer 1

To solve equations that involve radicals, you must square both sides of the equation.

Explanation:

`sqrt(x + 9)` = 4

`(sqrt(x +9))^2= (4)^2`

x + 9 = 16

x = 16 - 9

x = 7

With radical equations it is alway vital to check your solutions in the original equation, since extraneous solutions may arise. You must especially be careful of them in radical-quadratic equations, where two solutions often appear but oftentimes only one is the correct solution.

Practice exercises:

1. Solve each equation. Watch out for extraneous solutions.

a) `sqrt(2x + 5)` = 7

b) `sqrt(3x + 1)` = x - 3

c) `sqrt(2x + 2)` - `sqrt(x +2)` = 1

Answer 2

`x=7`

Explanation:

`sqrt(x+9)=4`

Square both sides:

`rarr(sqrt(x+9))^2=4^2`

`rarrx+9=16`

`rarrx=16-9=7`