Math Worksheets

Question: Algebra II Help – Radicals?

1. I need help. I’m supposed to find the extraneous root of:
sqrt(2x+20) + 2 = x
I know that the proper answer is x=8, but I don’t know how to find the root.

2. Select the number and type of solutions for the following equation: sqrt.(x^2-28)-1=x
I picked “no real roots”. Was I right? My other options are:
one extraneous root, two different real roots, a double root, three real roots.

3. Select the number and type of solutions for the following equation: n + sqrt(2n^2-28)=2

my options:
no real roots
two different real roots
a double root
three real roots
one real root, one extraneous root

I don’t even know how to find x for that one.

You don’t have to help with all of them, but those are the ones on the worksheet that I’m not sure about. Thank you in advance!

Answer: 1. sqrt(2x+20) + 2 = x
=> sqrt(2x+20) = x – 2, x > 2
Square both sides,
2x+20 = x^2-4x+4
=> x^2-6x-16 = (x-8)(x+2) = 0
x = 8
x = -2 rejected since x > 2

2. sqrt.(x^2-28)-1 = x
=> sqrt.(x^2-28) = x+1, x > -1
Square both sides,
x^2-28 = x^2+2x+1
=> 2x = -29
=> x = -14.5 rejected because x > -1.

3. n + sqrt(2n^2-28) = 2
=> sqrt(2n^2-28) = 2-n, n < 2
Square both sides,
2n^2-28 = 4-4n+n^2
=> n^2+4n-32 = (n+8)(n-4) = 0
n = -8
n = 4 is rejected since n < 2

Algebra 1 review worksheet for ch7 retake solutions videoB.avi