SOLUTION: square root of x+2 = 4 square root of x. I know the answer is 2/15 but I do not know how to solve this equation.

Click here to see ALL problems on Square-cubic-other-roots

Question 410299: square root of x+2 = 4 square root of x. I know the answer is 2/15 but I do not know how to solve this equation.
Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!
Please use parentheses around radicands (the expressions inside a radical are called radicands). The only reason I knew your equation is

and not

is that you gave the answer and it was easy to figure out which equation has that solution. Your equation can be unambiguously posted as:
square root of (x+2) = 4 square root of x
The second square root does not need parentheses (although they wouldn't hurt) because there is nothing after the x.

Tutors are more likely help if the problem is clearly stated.

Solving this equation is quite simple. Just square both sides:

which simplifies to:
x+2 = 16x
This equation is simple to solve. Subtracting x from each side we get:
2 = 15x
Dividing by 15 we get:
2/15 = x

Important: Whenever you square both sides of an equation, like we did, you must check your solution(s)! This is so because squaring both sides can introduce what are called extraneous solutions. Extraneous solutions are solutions that fit the squared equation but do not fit the original equation. These extraneous solutions can occur even if no mistakes have been made! SO even experts at Math have to check their solutions. If extraneous solutions are found during the check they are rejected.

Always us the original equation to check:

Checking x = 2/15:

which simplifies as follows:

Check!