Question

Show that√11 is an irrational number.

Answer 1

hey mate here is your answer..

A rational number can be written in the form of p/q where q ≠ 0 and p , q are non negative number.

√11 = p/q ....( Where p and q are co prime number )

Squaring both side !

11 = p²/q²

11 q² = p² ......( i )

p² is divisible by 11

p will also divisible by 11

Let p = 11 m ( Where m is any positive integer )

Squaring both side

p² = 121m²

Putting in ( i )

11 q² = 121m²

q² = 11 m²

q² is divisible by 11

q will also divisible by 11

Since p and q both are divisible by same number 11

So, they are not co - prime .

Hence Our assumption is Wrong √11 is an irrational number.

hope it helps you..

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Mark as brainlist..

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Answer 2

assume √11 is rational

√11= a/b( where a and b are number not co prime)

canceling common factord

√11=p/q(where p and q are co prime)

squaring both sides

(√11)²=(p/q)²

11=p²/q²

11q²=p²

therefore √11 divides p² as well as p

p=11×C

substituting p in 11q²=p²

11q²=(11c)²

11q²=121c²

q²=121c²/11

q²=11c²

therefore √11 divides q² as well as q

this is not possible as q and p are co prime

therefore √11 is an irrational number
pls do mark as brainliest. all the best for exams and feel free to ask doubts