Question

How do I find out if the square root of a number is irrational. I need this step by step so I can understand it! The numbers I want to find out this for is 81, 64, 16, and 10. @Hero Can you help, please? I don't want someone to give me the answer, I really wanna know this!

Answer 1

@mathstudent55 @jim_thompson5910 @ganeshie8 @Compassionate @johnweldon1993

Answer 2

I'll explain it a different way.

Answer 3

Please!

Answer 4

You still have to understand both ways of doing it either way. But there's a way to explain it with fractions.

Answer 5

ok

Answer 6

First of all, this is a rule (something to memorize and not necessarily to understand just yet):

\(\sqrt{n} = n^{1/2}\)

Answer 7

ok..i get that..

Answer 8

\(\sqrt{n^2} = (n^2)^{1/2} = n^{(2*1/2)} = n^{2/2} = n^1 = n\)

Answer 9

In short, the square root of n squared is n:
\(\sqrt{n^2} = n\)

Answer 10

So.... √81^2?

Answer 11

We're not there yet

Answer 12

You want to get to the goal line but you haven't ran the marathon yet.

Answer 13

k..

Answer 14

Here's what you (should) know:

\(1 \times 1 = 1\)
\(2 \times 2 = 4\)
\(3 \times 3 = 9\)
\(4 \times 4 = 16\)
\(5 \times 5 = 25\)
\(6 \times 6 = 36\)
\(7 \times 7 = 49\)
\(8 \times 8 = 64\)
\(9 \times 9 = 81\)

Answer 15

Similarly:

\(1^2 = 1\)
\(2^2 = 4\)
\(3^2 = 9\)
\(4^2 = 16\)
\(5^2 = 25\)
\(6^2 = 36\)
\(7^2 = 49\)
\(8^2 = 64\)
\(9^2 = 81\)

Answer 16

Are you with me so far?

Answer 17

Yes! :)

Answer 18

Also:

\(\dfrac{1^2}{1} = 1\)

\(\dfrac{2^2}{2} = 2\)

\(\dfrac{3^2}{3} = 3\)

\(\dfrac{4^2}{4} = 4\)

\(\dfrac{5^2}{5} = 5\)

\(\dfrac{6^2}{6} = 6\)

\(\dfrac{7^2}{7} = 7\)

\(\dfrac{8^2}{8} = 8\)

\(\dfrac{9^2}{9} = 9\)

Again, what you should know. If not, commit to memory.

Answer 19

kk...

Answer 20

81 is rational?

Answer 21

@Hero

Answer 22

81 - Rational
64 - Rational
16 - Rational
10 - Irrational

Is that right?
@Hero

Answer 23

@Hero

Answer 24

All of them are rational.

Answer 25

20/2 = 10

Answer 26

Every integer is rational

Answer 27

...All of them can't be rational...

Which of the following is an irrational number?
A. √81
B. √64
C. √16
D. √10

@Hero

Answer 28

That's not what you wrote the first time

Answer 29

\(10 \ne \sqrt{10}\)

Answer 30

That is what I wrote. I wanted to find out how to find out which one was irrational. -_-

Answer 31

10 is rational. \(\sqrt{10}\) is irrational. You're confusing yourself.

Answer 32

I know exactly what you wrote.

Answer 33

Woops, sorry. I admit defeat. :) I understand now. Sorry! Thanks for calling me out on it. :)

Answer 34

Thanks @hero Your the best!! :)

Answer 35

You know \(\sqrt{2}\) is irrational. Well \(\sqrt{10} = \sqrt{5 \times 2} = \sqrt{5}\sqrt{2}\)
\(\sqrt{10}\) includes \(\sqrt{2}\)

Answer 36

Would √11 be irrational?

Answer 37

11 is a prime number. The square root of a prime number is irrational.