Question

Given the equation Square root of 8x plus 1 = 5, solve for x and identify if it is an extraneous solution.

Answer 1

It depends if you mean
`√(8x) +1=5` or
`√(8x+1) = 5`


`√(8x) +1=5`

Subtract 1 from both sides.


`√(8x) =4`

Take the square root of both sides.

8x = sqrt(4)
8x = 2
x = 1/4.

Plugging it back in:
sqrt(8*0.25) + 1 = 5
sqrt(2) = 4

This is not true because the square root of 2 is about 1.41, which does not equal 4.
So it is an extraneous solution.
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`√(8x+1) = 5`
Square both sides.
8x + 1 = 25
8x = 24
x = 3

Not extraneous because equation works out when you plug x back in.