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

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Answer 1 · 2017-07-29T17:17:30

See two solution processes below:

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:

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

$x = 1024$

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