How can I get Mathematica to simplify my expression?

4.*^-12 Sqrt[3.0254210421890627*^22 - 6.25*^22 T6^2]

The above expression is equal to

Sqrt[0.48406736675024997 - T6^2]

How can I tell Mathematica to simplify the first form into the second form?

• Try FullSimplify[MapAt[Factor, yourExpression, {2, 1}]]. Jan 17, 2013 at 7:40
• @Silvia. Actually FullSimplify isn't needed; Simplify will do. Jan 17, 2013 at 7:54
• @m_goldberg Yes indeed. It's just my personal habit to use FullSimplify. Jan 17, 2013 at 10:15

Building on Silvia's comment:

expr = 4.*^-12 Sqrt[3.0254210421890627*^22 - 6.25`*^22 T6^2];

Rationalize[Factor //@ expr, 0] // Simplify
Sqrt[1936269467001/4000000000000 - T6^2]
% // N
Sqrt[0.484067 - 1. T6^2]

The 1. is an artifact of // N due to - T6^2 being internally Times[-1, Power[T6, 2]].

• Note: with V9, Rationalize isn't needed: Factor //@ expr // Simplify will do. Jan 17, 2013 at 8:16
• This does not work for 2. Sqrt[0.25 - b/3] . I just want all things are within Sqrt. Jan 17, 2013 at 8:38
• @goodluck try: Rationalize[2. Sqrt[0.25 - b/3], 0] // FullSimplify Jan 17, 2013 at 8:46
• @Mr.Wizard, it works for 0.25, but not work for 0.26. Jan 17, 2013 at 9:01
• @goodluck Is this a formatting issue? You are aware that Sqrt[9 x] will automatically simplify to 3 Sqrt[x], correct? Do you want a formatting rule like this? Jan 17, 2013 at 10:05