Math Is Fun Forum

paulb203

Member

Registered: 2023-02-24

Posts: 345

How to write √8 in the form 2^n

I struggled to do this but managed a guess of 2^1

My thinking was √8 = 2, and another way of writing 2 is 2^1

The answer given was 2^(3/2)

Which I understood, eventually, as meaning (√2)^3

which equals (√2)(√2)(√2)

which equals (√4)(√2)

which equals 2(√2)

which equals 2^1*2^(1/2)

which equals 2^1+(1/2)

which equals 2^(3/2)

My question is; are both correct? My answer at the top, and the one I was given?

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Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,820

Re: How to write √8 in the form 2^n

Hi paulb203,

is correct,

is not correct.

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amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: How to write √8 in the form 2^n

which equals 2^1*2^(1/2)

which equals 2^1+(1/2)

almost: add grouping symbols to keep the 1/2 in the power:

2^{1 + (1/2)}

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: How to write √8 in the form 2^n

The key to problems like this is

So start with

then

......(i)

So we have an answer, but it would be good to simplify it.

Substituting into (i) we get

Bob

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You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
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paulb203

Member

Registered: 2023-02-24

Posts: 345

Re: How to write √8 in the form 2^n

Thanks, guys.

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Prioritise. Persevere. No pain, no gain.