Question

How do you solve `sqrt(4x)=64` and check the solution?

Answer 1

See two solution processes below:

Explanation:

Process 1
First, square both sides of the equation to eliminate the radical while keeping the equation balanced:

`(sqrt(4x))^2 = 64^2`

`4x = 4096`

Now, divide each side of the equation by `color(red)(4)` to solve for `x` while keeping the equation balanced:

`(4x)/color(red)(4) = 4096/color(red)(4)`

`(color(red)(cancel(color(black)(4)))x)/cancel(color(red)(4)) = 1024`

`x = 1024`

Process 2
First, simplify the radical on the left using this rule:

`sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))`

`sqrt(4x) = 64`

`sqrt(color(red)(4) * color(blue)(x)) = 64`

`sqrt(color(red)(4))sqrt(color(blue)(x)) = 64`

`2sqrt(color(blue)(x)) = 64`

Now, divide each side of the equation by `color(red)(2)` to isolate the `x` term while keeping the equation balanced:

`(2sqrt(color(blue)(x)))/color(red)(2) = 64/color(red)(2)`

`(color(red)(cancel(color(black)(2)))sqrt(color(blue)(x)))/cancel(color(red)(2)) = 32`

`sqrt(color(blue)(x)) = 32`

Now, square both sides of the equation to eliminate the radical and solve for `x` while keeping the equation balanced:

`(sqrt(color(blue)(x)))^2 = 32^2`

`x = 1024`