Solving for "a" in Square Root Equation

In summary, the conversation discusses finding the value of a in an equation involving square roots. The solution involves squaring both sides of the equation and using the formula for (a+b)^2. The final solution is 12 + √(36-a) = 14.
  • #1
Asla
35
0

Homework Statement


Get the value of a if
[itex]\sqrt{6-\sqrt{a}}[/itex]+[itex]\sqrt{6+\sqrt{a}}[/itex]=[itex]\sqrt{14}[/itex]


The Attempt at a Solution


nothing succesfull
Feel free to move this thread,..I actually place it here to tap more brains
 
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  • #2
square? :wink:
 
  • #3
tiny-tim said:
square? :wink:
What do you mean?I square both sides?
 
  • #4
square as many sides as you can find! :biggrin:
 
  • #5
tiny-tim said:
square as many sides as you can find! :biggrin:
It gives me this:
12+[itex]\sqrt{36-a}[/itex]=14
could I be going wrong somewhere?
 
  • #6
Damn it I had never felt so foolish,..thanks I got it
 
  • #7
Asla said:
It gives me this:
12+[itex]\sqrt{36-a}[/itex]=14
could I be going wrong somewhere?

(a+b)² = a² + 2ab + b²

Nevermind. You've already gotten it!
 

What is a square root equation?

A square root equation is an equation in which the variable is located inside a square root symbol. The goal of solving a square root equation is to isolate the variable and find its value.

How do I solve for "a" in a square root equation?

To solve for "a" in a square root equation, you will need to use inverse operations to isolate the variable. This means performing the opposite operation of what is being done to the variable. For example, if the variable is being multiplied by a number, you would divide both sides by that number to isolate the variable.

What are some common mistakes when solving for "a" in a square root equation?

Some common mistakes when solving for "a" in a square root equation include forgetting to perform the inverse operation, not simplifying the square root on the other side of the equation, and forgetting to check for extraneous solutions.

What should I do if I end up with "a = 0" when solving a square root equation?

If you end up with "a = 0" when solving a square root equation, this means that the equation has no real solutions. This could be because the original equation has no real solutions, or because you made a mistake during the solving process.

Can I solve for "a" in a square root equation using the quadratic formula?

Yes, you can solve for "a" in a square root equation using the quadratic formula. However, this is not always necessary and may result in more complex solutions compared to using inverse operations. It is important to choose the most efficient method for solving a square root equation depending on the complexity of the equation.

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