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Do you have an intuition about rational and irrational number ?
What is that supposed to mean
What is your mother toungue ?
That makes no sense
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
Is pi a rational or irrational number ?
What about 0.5 ?
i hope you understand it now :)
So, 0.817643 is rational or irrational ?
See, 0.5 =1/2 so rational.
Thanks anyways I got it
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...
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
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.
4. Estimate √58 to the nearest integer. Are you allowed a calculator? Or did they give you a way to do this problem?
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
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