We have a math competition tomorrow. I think it's national or provincial, I'm not sure. But I'm one of the students that gets to take part in it. I'm up against all grade 8's.
So, on the practise sheet there's this one question.... And I can't, for the life of me, figure out how to do it. And I cannot use a calculator.
Please do not give me the answer. I need to figure it out for myself.
Question:
What is the largest positive integer n satisfies n^200 < 3^500?
I know what exponents are, but it's just that the exponent is so large. I have no clue how to figure it out. So, how would I figure out what 3^500 is? Please don't tell me what n is though, I need to figure it out on my own :)
Thank you!
So, on the practise sheet there's this one question.... And I can't, for the life of me, figure out how to do it. And I cannot use a calculator.
Please do not give me the answer. I need to figure it out for myself.
Question:
What is the largest positive integer n satisfies n^200 < 3^500?
I know what exponents are, but it's just that the exponent is so large. I have no clue how to figure it out. So, how would I figure out what 3^500 is? Please don't tell me what n is though, I need to figure it out on my own :)
Thank you!
-
3^500 = 3^(200*2.5) = (3^2.5)^200
3^2.5 = 3^(5/2) = Sqrt(3^5) = Sqrt(3*81) = Sqrt(243)
Square root 243 :
2|43 | 15.x
--------
1|00 | 1
---------
143 | 25x5=125, 26x6=120+36>143
125 |
----------
18
...
hence the number is n=15
3^2.5 = 3^(5/2) = Sqrt(3^5) = Sqrt(3*81) = Sqrt(243)
Square root 243 :
2|43 | 15.x
--------
1|00 | 1
---------
143 | 25x5=125, 26x6=120+36>143
125 |
----------
18
...
hence the number is n=15