# Applying square root to equation [duplicate]

I want to apply square root operation to an equation.

In[1]:= Equation := x^2 == 2 y;

In[2]:= Sqrt[Equation]


Here is the output:

My goal is to simplify this expression, so as it would take Root of the left and right parts separately

How can I do that?

• Please copy the code not the image. Have you tried something? – L.K. Apr 24 '17 at 16:20
• The image represents the output, not the code itself. Yes. I tried using Simplify function, but with no result. – Elias Apr 24 '17 at 16:27
• We need code to simplify the expression. You have to provide the code, so that we can work on that. – L.K. Apr 24 '17 at 16:31
• I've updated the question. – Elias Apr 24 '17 at 16:40
• You'd eventually be trying to take the square root of True or False, no? – MikeY Apr 24 '17 at 16:57

It's generally not a good idea to start your symbol names with an uppercase letter and you should look at the difference between SetDelayed, i.e. := and Set, i.e. =.

That said, one answer to your question is to use Map (/@ below) to apply Sqrt to both sides of your equation and add an assumption to Simplify to allow it to simplify Sqrt[x^2] to x which is what I assume you want.

eqn = x^2 == 2 y;
Simplify[Sqrt /@ eqn, x > 0]


x == Sqrt[2] Sqrt[y]

If you don't want this then Solve[eqn, x], gives an alternative form as stated by others.

Thread[] is one of the classical ways to do this operation:

Thread[Sqrt[x^2 == 2 y], Equal]
Sqrt[x^2] == Sqrt[2] Sqrt[y]

Solve[x^2 == 2 y, {x}]

{{x -> -Sqrt[2] Sqrt[y]}, {x -> Sqrt[2] Sqrt[y]}}

• I must have been a time traveler. ;) I answered it 33 minutes ago and Mike answered it 22 minutes ago. – UnchartedWorks Apr 24 '17 at 17:33
• Right, accept my apologies. :) – Kuba Apr 24 '17 at 17:35