Question

Steps for solving radical equations?

Answer 1

The question I'm working with is
\[\sqrt{x-3}+\sqrt{x+2}=5\]

Answer 2

I need the steps

Answer 3

isolate the radical
square each side
foil
simplify
square
simplify/solve
check
IS THIS CORRECT

Answer 4

these pretty much suck, because you are going to have to square twice

Answer 5

1. Isolate the radical expression.

2. Square both sides of the equation: If x = y then x2 = y2.

3. Once the radical is removed, solve for the unknown.

4. Check all answers.

Answer 6

you want a quick method?

Answer 7

Always check back your answers because the radical/square can always hide a negative in the squaring process.

Answer 8

the steps i listed were the ones i saw when going over my review key

Answer 9

quick method is to look at \(\sqrt{x+2}\) and ask what would make the number inside a perfect square
\(x=2\) would work because \(2+2=4\) but it won't work for \(\sqrt{x-3}\)
\(x=7\) works because \(7+2=9\) so lets try that one
\[\sqrt{7-3}+\sqrt{7+2}=\sqrt{4}+\sqrt{9}=2+3=5\] got it on the second guess

Answer 10

i'd prefer the other way i listed if it is correct

Answer 11

if you don't like the thinking method you have to write
\[\sqrt{x-3}+\sqrt{x+2}=5\\
\sqrt{x-3}=5-\sqrt{x+2}\] then square both sides (carefully) and get
\[x-3=25-10\sqrt{x+2}+x+2\] then combine like terms on the rigth
\[x-3=27+x-10\sqrt{x+2}\] isolate the radical and get
\[-30=-10\sqrt{x+2}\\
3=\sqrt{x+2}\]

Answer 12

now square again and get
\[9=x+2\] and so \(x=7\)
but really this is long an involved
i know most people, especially math teachers, like "step step step..." but it never hurts to think first
maybe you get it right away

Answer 13

i have to show all rhe work that is the only issue

Answer 14

i guess you can't show "thinking"
any decent math teacher would be pleased at finding an answer from dint of sheer brain power, but whatever
all steps are above

Answer 15

thank you