Math Is Fun Forum

paulb203

Member

Registered: 2023-02-24

Posts: 345

Surds. Division Rules.

Why does, 4√64÷2√4
=2√16 ?

I can see the method (4÷2=2, √64÷√4=√16)

But why is it not;

4 times √64 divided by 2 times √4 (as per BODMAS)
i.e, 4 times 8 divided by 2 times 2, which = 32

Nb. When I put it into my calculator that way it gives 32 as the answer
(4*√64÷2*√4)

Last edited by paulb203 (2023-10-29 06:15:29)

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Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,820

Re: Surds. Division Rules.

Hi,

BODMAS: Brackets Orders Division Multiplication Addition Subtraction.
Brackets make a difference.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Surds. Division Rules.

hi paulb203

4√64÷2√4

The problem here is that it is not clear whether this means

or

The BODMAS rules do not 'attach' the 2 and root 4 as an item to be calculated before the division so, in my view, there is an implied multiplication here 2√4 ie 2 x √4 and therefore the second calculation is correct.

If this appeared in a book it should have had extra brackets like my top calculation.

See https://www.mathsisfun.com/algebra/oper … lator.html

with the entry 4sqrt(64)÷2sqrt(4). MIF gives this as 32.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

paulb203

Member

Registered: 2023-02-24

Posts: 345

Re: Surds. Division Rules.

Hi,

BODMAS: Brackets Orders Division Multiplication Addition Subtraction.
Brackets make a difference.

Thanks. Why have you added brackets?

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Prioritise. Persevere. No pain, no gain.

paulb203

Member

Registered: 2023-02-24

Posts: 345

Re: Surds. Division Rules.

Thanks, Bob.

I'm getting the impression that BODMAS is for primary and secondary school maths, but at the more advanced level of degree and post graduate it doesn't really apply as maths problems at that level are set out unambiguously, e.g, instead of the division symbol you would have a slash; you wouldn't have the times symbol (x) you would have brackets instead, or the multiplication would be implied by juxtaposition (e.g, a number directly in front of brackets).

I spoke to a few others online about this, each of whom got annoyed at the mere question, as they were sick of what they regarded as, 'all this BODMAS' nonsense.

It made me think, Who sets the agenda? And why don't the early years educators get together with the more advanced people and create an objective standard?

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Prioritise. Persevere. No pain, no gain.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,820

Re: Surds. Division Rules.

Hi paulb203,

BODMAS is Brackets, Orders, Division, Multiplication, Addition, Subtraction.

Brackets are for convenience. Here, these are for calculations although they don't appear in the problems.

Ignoring the brackets in the solution I had given, the operations Exponentiation/Roots, Division/Multiplication, Addition/Subtraction.

Jai.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Surds. Division Rules.

Wolfram Alpha gives 32 as well.

https://www.wolframalpha.com/input?i=ev … %E2%88%9A4

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,820

Re: Surds. Division Rules.

Hi,

I checked with my Scientific Calculator and confirmed the actual solution is 32, not 8. I have complete trust in my Scientific Calculator. I stand corrected.

Jai Ganesh.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,893

Re: Surds. Division Rules.

This is from MIF's Order of Operations...PEMDAS (same as BODMAS) page:

Substituting variables for the number components, Mathematica (like WolframAlpha) simplifies the expression like this...

...and like this:

When giving the {a,b,c,d} variables their respective {4,64,2,4} values, Mathematica returns the answer 32.

Last edited by phrontister (2023-10-30 18:42:07)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

paulb203

Member

Registered: 2023-02-24

Posts: 345

Re: Surds. Division Rules.

Thanks, guys.

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Prioritise. Persevere. No pain, no gain.