Applying square root to equation

Question

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
You'd eventually be trying to take the square root of True or False, no? — MikeY, Apr 24 '17 at 16:57
@L.K., nope, I didn't want to solve it, but rather simplify the equation for further processing. — Elias, May 06 '17 at 11:21

score 2 · Accepted Answer · answered Apr 24 '17 at 17:09

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.

score 2 · Answer 2 · answered Apr 25 '17 at 02:18

2

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]

answered Apr 25 '17 at 02:18

J. M.'s missing motivation

124,525
11
401
574

score 1 · Answer 3 · edited Apr 24 '17 at 17:23

1

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

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

edited Apr 24 '17 at 17:23

Kuba

136,707
13
279
740

answered Apr 24 '17 at 16:58

webcpu

3,182
12
17

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

Applying square root to equation

3 Answers3