Question

Show that root7 is irrational number

Answer 1

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Let √7 be rational number
Then, √7 = p/q
Here, p and q are integers and q is unequal to zero and there is no any common divisor between p and q except 1.

Now, √7 = p/q

$7 = {p}^{2} \div \: {q}^{2}$
${p}^{2} = \: 7{q}^{2}$

From above, it is clear that 7 will divide p.
Let p=7m (where m is any integer)
So, p^2 = 7 q^2
=> (7m)^2 = 7q^2
=> 49 m^2 = 7q^2
=> 7 m^2 = q^2
Hence, q is also divisible by 7.


THEREFORE, 7 IS A COMMON DIVISOR BETWEEN BOTH "p" AND "q" WHICH CONTRADICT OUR ASSUMPTION.

THUS, √7 IS IRRATIONAL NUMBER.........


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