AS Maths - root numbers! Someone help?

Ok, so I was doing a past paper and really panicked when I came across this question. I'm probably being silly but I always have trouble when having to root numbers (that are higher than square roots, and 3rd roots).

e.g. fifth root of 32 (taken from part 'a' the following question)...
C1 June 2012 Q2(a) root numbers.png

Can someone link a video or explain to me the procedure of rooting numbers please? :frown:

(edited 7 years ago)

Reply 1

Kevin De Bruyne

21

Original post by Philip-flop

Ok, so I was doing a past paper and really panicked when I came across this question. I'm probably being silly but I always have trouble when having to root numbers (that are higher than square roots, and 3rd roots).

e.g. fifth root of 32 (taken from the following question)...
C1 June 2012 Q2(a) root numbers.png

I'm not sure if they'd ever give you a disgusting number to work with. Eg fifth root of 234.

So perhaps it's worth checking numbers like 2,3,4 etc. After all, you know that 32^0.6 is going to be less than 32^1 so the 5fth root can't be that big.

Reply 2

username1628823

19

You're expected to know 2 to any index. 32 is 2^32. I haven't seen them use powers higher than three for any other number, but if they do, try to figure it out.

Reply 3

Zacken

22

Original post by Jasaron

You're expected to know 2 to any index. 32 is 2^32. I haven't seen them use powers higher than three for any other number, but if they do, try to figure it out.

32 is not 2^32. :tongue:

Reply 4

Zacken

22

Original post by Philip-flop

Ok, so I was doing a past paper and really panicked when I came across this question. I'm probably being silly but I always have trouble when having to root numbers (that are higher than square roots, and 3rd roots).

Can someone link a video or explain to me the procedure of rooting numbers please? :frown:

At this level, you'll need to realise that "rooting" numbers in the exam means looking for a way to represent the given number in a different format such that the rooting process becomes easy.

So, you'll see

32^{1/5}

and you should be thinking "what ways can I represent 32 as a number to the power 5 (or to the power 10 or to the power 15, etc... so that the power cancels the root nicely". In this case, it's particularly easy because there aren't many possible numbers. 3^5 is far bigger than 32, 2^10 is far bigger than 32, so the only possible thing is 2^5, really.

Then:

(2^5)^{1/5} = 2^{5/5} = 2.

Reply 5

Philip-flop

OP

18

Original post by Zacken

At this level, you'll need to realise that "rooting" numbers in the exam means looking for a way to represent the given number in a different format such that the rooting process becomes easy.

So, you'll see

32^{1/5}

and you should be thinking "what ways can I represent 32 as a number to the power 5 (or to the power 10 or to the power 15, etc... so that the power cancels the root nicely". In this case, it's particularly easy because there aren't many possible numbers. 3^5 is far bigger than 32, 2^10 is far bigger than 32, so the only possible thing is 2^5, really.

Then:

(2^5)^{1/5} = 2^{5/5} = 2.

Wow, thanks @Zacken!! You giving me a different perspective/ way of looking at it has made this so much clearer in how to tackle these kind of problems :smile: