# Solving sqrt (Y+6) - sqrt (3y) = 3

• perpetual-burn
In summary, the conversation involves someone asking for help in solving an equation and another person providing instructions on how to solve it. The first step is to square both sides of the equation, and then isolate the square root on one side and square again. The second person also reminds the first person to check if the solutions they get are larger than 0.

#### perpetual-burn

Hey guys,
I was wondering how to solve this equation. I tihnk I got it, but I want to make sure so I don't go on doing all of my homework wrong.

Question: sqrt (Y+6) - sqrt (3y) = 3

I forget if I have to sqaure each separate or the whole left side as FOIL. Please let me knwo asap so I can finish homeowkr :) Again, thanks so much!

-Phil

U'll have to square twice.And each time separate a sqrt in one side of the equation.

$$\sqrt{y+6}-\sqrt{3y}=3\Rightarrow y+6+3y-2\sqrt{\left(y+6\right)3y}=9$$

and then isolate in one member of the equation that sqrt and then square again.

Daniel.

Ok, waht i tohught :) Thanks Dan.

I hope u can solve the quadratic that will follow.And to check whether the solutions u get are larger than 0...

Daniel.

## 1. What is the first step in solving this equation?

The first step in solving this equation is to isolate the square root terms on one side of the equation. In this case, we can start by subtracting sqrt(3y) from both sides.

## 2. How do I handle the square roots on the left side of the equation?

To handle the square roots on the left side, we can use the property of square roots which states that sqrt(a) - sqrt(b) = sqrt(a-b). This allows us to rewrite the equation as sqrt(Y+6 - 3y) = 3.

## 3. What do I do next after isolating the square root term?

Next, we can square both sides of the equation to eliminate the square root on the left side. This gives us Y+6 - 3y = 3^2, which simplifies to -2y = -3.

## 4. How do I solve for y after simplifying the equation?

To solve for y, we divide both sides by -2 to isolate y. This gives us y = (-3)/(-2) = 1.5.

## 5. Is 1.5 the only solution to this equation?

Yes, in this case, 1.5 is the only solution to the equation. However, when solving equations with square roots, it's important to check for extraneous solutions by plugging the found value back into the original equation to ensure it satisfies the equation.