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1. 0.817643 = rational or irrational 2. -√88 rational or irrational 3. -√169 rational or irrational 4. Estimate √58 to the nearest integer. Help! Thank you!

Mathematics
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  • hba
Do you have an intuition about rational and irrational number ?
ummmm
What is that supposed to mean

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Other answers:

  • hba
What is your mother toungue ?
That makes no sense
  • hba
Let me rephrase it for you, Do you know what a rational and irrational number is ?
any number with terminating decimals is a rational number ,but those numbers having not-terminating(maybe repeating) decimals are irrational numbers.
Yes I do
  • hba
Is pi a rational or irrational number ?
irrational
  • hba
What about 0.5 ?
rationsl
good :)
i hope you understand it now :)
  • hba
So, 0.817643 is rational or irrational ?
Thanks
rational
  • hba
See, 0.5 =1/2 so rational.
right
Thanks anyways I got it
  • phi
rational means you can write it down as a decimal. irrational means the decimals keep going, never repeating, no rhyme or reason for what the next decimal will be pi is a good example. roots (in general) are irrational unless they are roots of perfect squares. example square root of 4 is 2 but sqrt(5) is irrational. btw, same idea for cube roots, etc...
Thankies!! :)
  • phi
The trick part in these questions is recognizing that a number is a perfect square. 169 is 13*13, so the square root of 169 is 13, and rational
  • phi
88 is 2*44 or 2*2*2*11 and so sqrt(88)= sqrt(2*2*2*11)= sqrt(2*2)*sqrt(2*11)= 2sqrt(22) and sqrt(22) is irrational, and 2 times an irrational is still irrational.
  • phi
4. Estimate √58 to the nearest integer. Are you allowed a calculator? Or did they give you a way to do this problem?
calculator
  • phi
find the square root, and round to the nearest whole number. to round, look at the digit in the tenths place (next to the decimal point) if 4 or less, drop the decimals and that is the answer if 5 or bigger, drop the decimals, but ADD 1 to the answer example: 100.3 to the nearest integer is 100 (3 is 4 or less, so drop the decimals) 210.50013 to the nearest integer is 210+1 (because 5 is 5 or bigger) you get 211
Alrighty thank you
  • phi
if you are not allowed a calculator, write down the squares near 58 7*7 is 49 58 is between them 8*8 is 64 58 is 9 away from 49 and 6 away from 64. so 58 is closer to 64 than it is to 49 that is a clue that sqrt(58) is closer to 8 than to 7

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