Re: SameQ to check for simplified radical expressions... doesn't work

• To: mathgroup at smc.vnet.net
• Subject: [mg120976] Re: SameQ to check for simplified radical expressions... doesn't work
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Sat, 20 Aug 2011 06:15:57 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```Here are your three expressions:

{Simplify[Sqrt[360]], Sqrt[360], Hold[6*Sqrt[10]]}

{6 Sqrt[10], 6 Sqrt[10], Hold[6 Sqrt[10]]}

As you can see, the first two are identical, and the third is not.

So the "problem" is that Simplify isn't doing anything.

Now consider:

FullForm@Sqrt[360]
Times[6,Power[10,Rational[1,2]]]

Now imagine this one with 360 in place of 10:

FullForm@Sqrt[10]
Power[10,Rational[1,2]]

LeafCount /@ {Sqrt[360], Sqrt[10]}

{7, 5}

ByteCount /@ {Sqrt[360], Sqrt[10]}

{264, 184}

The second is obviously simpler, hence Sqrt[360] is simpler than 6
Sqrt[10].

But Mathematica doesn't see it that way, and apparently, neither do you.

Bobby

On Fri, 19 Aug 2011 05:33:06 -0500, Roy Simpson <roy at mathemaddicts.com>
wrote:

> Hello,
>
> I have what appears to be a simple issue, but I cannot for the life of
> me figure it out.  I will have a randomized number, a, and I am going to
> simplify the square root of this.  Then I want to compare this to a
> radical expression that a student enters, say b.  Thus, the idea should
> be something like
>
> Simplify[Sqrt[a]] === Sqrt[b]
>
> For sake of this example, let's suppose the number I want to consider is
> the square root of 360.  I only want the statement to return TRUE if the
> rhs of this SameQ is exactly 6*Sqrt[10].
>
> Unfortunately,
>
> Simplify[Sqrt[360]] === Sqrt[360]
> returns TRUE.
>
> I tried a few variations with Hold, but they always return false if the
> student enters the correct answer.  For example, if the student entered
> 6*Sqrt[10], then
>
> Simplify[Sqrt[360]] === Hold[6*Sqrt[10]]
> returns FALSE
>
> What am I doing wrong?  Any help would be appreciated.
>

--
DrMajorBob at yahoo.com

```

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