Question

help :)

Answer 1

Find the solution of \[\sqrt{x + 3 + 6} = 9 \] and determine if it is an extraneous solution.


x = 0; extraneous
x = 0; not extraneous
x = 6; extraneous
x = 6; not extraneous

Answer 2

@freckles

Answer 3

is that 6 really underneath the square root?

Answer 4

no

Answer 5

\[\sqrt{x+3}+6=9\]
so you mean this?

Answer 6

First step subtract 6 on both sides.
After that square to get rid of the square root.

Answer 7

\[\sqrt{x+3}=9-6\]
square both sides after simplifying the right hand side

Answer 8

yup and im not good at sqrt...

Answer 9

do you know how to square both sides?

Answer 10

no

Answer 11

(sqrt(x+3))^2 is just equal to x+3
that is why we are squaring both sides

Answer 12

\[(\sqrt{x+3})^2=(9-6)^2\]
\[x+3=(9-6)^2\]
see if you finish solving this

Answer 13

x + 3 = 9
- 3 - 3
x = 6?

Answer 14

yes
now check the solution
if x=6 doesn't work then the solution is not really a solution and consider an extraneous solution
if x=6 does work then the solution is not extraneous

Answer 15

\[\sqrt{x+3}+6=9\]
replace x with 6

Answer 16

so i plug in 6 into the original equation?

Answer 17

okay give me a sec

Answer 18

i got 9 = 9

Answer 19

9=9 is totally true

Answer 20

because 9 is in fact 9

Answer 21

so that means the solution works

Answer 22

and according to my if then statements the x=6 in non-extran

Answer 23

yeap so it will be if x= 6 not extraneous

Answer 24

yep

Answer 25

k thnx your really good at explaining is it okay if you help me with more?

Answer 26

so here is another one:
\[\sqrt{x-3}=10 \\ \text{ \square both sides to get rid of the square root } \\ x-3=10^2 \\ x-3=100 \\ x=103 \\ \]
and then you can check it
this showing you another with a square root

Answer 27

\[(\sqrt{x})^2=x\]

Answer 28

the square on the outside will just cancel the square root thing inside

Answer 29

should I plug in the 103 into the original equation and solve for the one you made?

Answer 30

sure to determine if it is extran or non-extran

Answer 31

it is not extran because 10 = 10 so for this the answer would be x = 103 non extran

Answer 32

yes you will end up with 10=10
which is a true statement
so x=103 is non-extran
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I think I can help with one more question
then I eat pizza

Answer 33

lol okay but it's a little different should i open it in new tab?

Answer 34

I can think of one that will give you extran
\[\sqrt{x-2}=-11 \\ x-2=(-11)^2 \\ x-2=121 \\ x=121+2 \\ x=123 \\ \text{ \check } \sqrt{123-2}= \sqrt{121}=11 \neq -11 \text{ so since } 11 \neq -11 \\ x=123 \text{ is extran }\]

Answer 35

open a new tab just in case I have to go