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Why is this Correct???

Hi, can somebody just tell me why this is right please?
Question: Evaluate (1 9/16) ^3/2. The answer is plus or minus 125/64.
Can somebody tell me why? Thanks.
Reply 1
Yes probably
Reply 2
Edit to potentially save (some) dignity
(edited 12 years ago)
Reply 3
Remember it's (1 and 9 16ths) to the power of 3/2
Reply 4
Oh, I assumed that was a typo (meaning something like question 1)).

In which case, 1 and 9/16 is the same as 25/16. And that does work. What's the issue you have with it. If it is to the power 3/2, then you can separate it into ((25/16)^1/2)^3. Then it follows.

It's maybe not obvious why it works, but it's rather difficult to know where your problem lies :smile:
Start by writing it as a single fraction...

1916=25161\frac{9}{16}=\dfrac{25}{16}

then just apply the square root and cube separately:

(2516)32=(2516)3=(±54)3=±12564\left(\dfrac{25}{16}\right)^{ \frac{3}{2}} = \left(\sqrt{\dfrac{25}{16}} \right) ^3= \left( \pm \dfrac{5}{4} \right)^3 = \pm\dfrac{125}{64}
Reply 6
Remember when you sqaure root something it's plus or minus
Reply 7
1 and 9/16 = 16/16 + 9/16 = 25/16

25/16^3/2 = ((25/16)^3)^1/2 = (25^3 / 16^3)^1/2 = (15625/4096)^1/2 = (15625^1/2) / (4096^1/2) = 125/64
Reply 8
Original post by Chwirkytheappleboy
Start by writing it as a single fraction...

1916=25161\frac{9}{16}=\dfrac{25}{16}

then just apply the square root and cube separately:

(2516)32=(2516)3=(±54)3=±12564\left(\dfrac{25}{16}\right)^{ \frac{3}{2}} = \left(\sqrt{\dfrac{25}{16}} \right) ^3= \left( \pm \dfrac{5}{4} \right)^3 = \pm\dfrac{125}{64}


Perfecto!
Reply 9
No calculators allowed
Original post by Horchata
1 and 9/16 = 16/16 + 9/16 = 25/16

25/16^3/2 = ((25/16)^3)^1/2 = (25^3 / 16^3)^1/2 = (15625/4096)^1/2 = (15625^1/2) / (4096^1/2) = 125/64
Reply 10
Original post by Horchata
1 and 9/16 = 16/16 + 9/16 = 25/16

25/16^3/2 = ((25/16)^3)^1/2 = (25^3 / 16^3)^1/2 = (15625/4096)^1/2 = (15625^1/2) / (4096^1/2) = 125/64


Hi
With all due respect that is a very laboured way of looking at the question.
Taking the half power will always first be far easier.
Reply 11
Square root, then to the power of 3.
Original post by POWW!
Remember when you sqaure root something it's plus or minus


I'm afraid not. The answer to this question (as given) is incorrect and should just be positive.

To clarify:

x2=25x^2 = 25 has two answers (this is where you need to remember the plus or minus).

x=25x=\sqrt{25} has one answer.
Original post by Mr M
I'm afraid not. The answer to this question (as given) is incorrect and should just be positive.

To clarify:

x2=25x^2 = 25 has two answers (this is where you need to remember the plus or minus).

x=25x=\sqrt{25} has one answer.


Proof for this?
Reply 15
It isn't plus or minus! By definition the square root sign takes the POSITIVE square root.
Original post by rorydaredking
Proof for this?


For analogy simply consider the function f(x)=exf(x)=e^x, which is always non-negative and monotonically increasing.

Specifically e32>0e^{\frac{3}{2}} > 0

It's a similar argument for all positive numbers aa with regards to the function g(x)=axg(x) =a^x, which is why only the positive sign holds here.

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