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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?

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3  
Try FullSimplify[MapAt[Factor, yourExpression, {2, 1}]]. – Silvia Jan 17 at 7:40
@Silvia. Actually FullSimplify isn't needed; Simplify will do. – m_goldberg Jan 17 at 7:54
@m_goldberg Yes indeed. It's just my personal habit to use FullSimplify. – Silvia Jan 17 at 10:15

1 Answer

up vote 2 down vote

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]].

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1  
Note: with V9, Rationalize isn't needed: Factor //@ expr // Simplify will do. – m_goldberg Jan 17 at 8:16
This does not work for 2. Sqrt[0.25 - b/3] . I just want all things are within Sqrt. – goodluck Jan 17 at 8:38
@goodluck try: Rationalize[2. Sqrt[0.25 - b/3], 0] // FullSimplify – Mr.Wizard♦ Jan 17 at 8:46
@Mr.Wizard, it works for 0.25, but not work for 0.26. – goodluck Jan 17 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? – Mr.Wizard♦ Jan 17 at 10:05

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