i have this question on my homework and i can't figure it out.
2006-09-07 10:44:18 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Yes! It cannot be represented as a ratio of integers a/b... you can't break 11 down any further (it's prime) so you can't write √11 as a ratio of integers (a fraction).
The person above is not truly correct about looking at your calculator. Say I asked you if √(1/49) was rational or not. Put this in your calculator and you'll get: 0.142857... repeating. This is actually the decimal form of 1/7. And 1/7 is a fraction. So √(1/49) *is* rational, but √11 is irrational.
For the square root of a number to be rational, you must be able to put it in a form where the numerator and denominator are both perfect squares. Then the square root will be a fraction.
11 can't be represented as a fraction with perfect squares. So √11 is not rational. √(25/4) is a fraction with perfect squares so √(25/4) = 5/2 and is therefore rational.
Yes, √11 is an irrational number.
2006-09-07 10:48:54 · answer #1 · answered by Puzzling 7 · 1⤊ 0⤋
Indeed it's irrationnal. The proof must be almost the same as the one concerning the square root of two...
I'll try and give you the idea :
let's assume that it's a rational number, it means that you can write :
sqrt(11)=a/b where gcd(a,b)=1
Thus, 11=a²/b² and then 11a²=b²
This means that 11 divides b², and, as it is a prime number, it divides b. Rewrite b:=11c, you obtain :
11a²=11*11c² which gives a²=11c²
Thus, 11 divides a², and, as 11 is prime, it divides a. Then gcd(a;b)>=11
This is absurd as we supposed it was one.
I think that should be correct but check it 'cause my english sometimes sucks :p
2006-09-07 17:54:54 · answer #2 · answered by Snouffa 1 · 2⤊ 0⤋
Yes, it's irrational. In fact, the square root of any
non-square whole number is irrational.
2006-09-07 18:08:55 · answer #3 · answered by steiner1745 7 · 0⤊ 0⤋
An irrational number is any number has decimal places that do not repeat. Based on my initial observation Squrt(11)=3.31662479036 is irrational.
2006-09-07 18:48:09 · answer #4 · answered by Scott S 4 · 0⤊ 0⤋
So following on the from the previous answer... yes, as it cannot be expressed as a fraction.
2006-09-07 17:49:55 · answer #5 · answered by bob s 1 · 0⤊ 0⤋
yes
2006-09-07 17:53:41 · answer #6 · answered by the ghost 2 · 0⤊ 0⤋
put it into your calculator. you will see that it is a repeating decimal similar to pi.
2006-09-07 17:47:46 · answer #7 · answered by elmo o 4 · 0⤊ 1⤋