Question

Show that
$\sqrt{11}$
is an irrational
number
$\sqrt{11 \\ }$
​

Answer 1

Answer:

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Answer:

Let us assume that √2 is a rational number.

then, as we know a rational number should be in the form of p/q

where p and q are co- prime number.

So,

√2 = p/q { where p and q are co- prime}

√2q = p

Now, by squaring both the side

we get,

(√2q)² = p²

2q² = p² .( i )

So,

if 2 is the factor of p²

then, 2 is also a factor of p .( ii )

=> Let p = 2m { where m is any integer }

squaring both sides

p² = (2m)²

p² = 4m²

putting the value of p² in equation ( i )

2q² = p²

2q² = 4m²

q² = 2m²

So,

if 2 is factor of q²

Then 2 is also factor of q

Since

2 is factor of p & q both

So, our assumption that p & q are co- prime is wrong

Hence √2 is an irrational number

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Answer 2

square root of prime numbers is always irrational number.

Irrational number has non- terminating and non-recurring decimal.