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

Question

Genesis Allen · Accepted Answer

See two solution processes below:

Procedure 1: To remove the radical and maintain the equation's balance, first square both sides of the equation: #(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: Applying the following rule, first simplify the radical on the left: #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#

Eva Abramson · Answer

undefined To solve the equation sqrt(4x) = 64, we need to isolate the variable x.

First, square both sides of the equation to eliminate the square root: (sqrt(4x))^2 = 64^2.

This simplifies to 4x = 4096.

Next, divide both sides of the equation by 4 to solve for x: x = 4096/4.

Simplifying further, x = 1024.

To check the solution, substitute x = 1024 back into the original equation sqrt(4x) = 64.

sqrt(4 * 1024) = 64.

sqrt(4096) = 64.

64 = 64.

Since both sides of the equation are equal, the solution x = 1024 is correct.