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!

- anonymous

- schrodinger

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- hba

Do you have an intuition about rational and irrational number ?

- anonymous

ummmm

- anonymous

What is that supposed to mean

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## More answers

- hba

What is your mother toungue ?

- anonymous

That makes no sense

- hba

Let me rephrase it for you,
Do you know what a rational and irrational number is ?

- AravindG

any number with terminating decimals is a rational number ,but those numbers having not-terminating(maybe repeating) decimals are irrational numbers.

- anonymous

Yes I do

- hba

Is pi a rational or irrational number ?

- anonymous

irrational

- hba

What about 0.5 ?

- anonymous

rationsl

- AravindG

good :)

- AravindG

i hope you understand it now :)

- hba

So, 0.817643 is rational or irrational ?

- anonymous

Thanks

- anonymous

rational

- hba

See, 0.5 =1/2 so rational.

- anonymous

right

- anonymous

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...

- anonymous

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?

- anonymous

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

- anonymous

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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