Question

solve this by long division method ​

Answer 1

Answer:

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Step-by-step explanation:

Irrational

Here, 7  is not a perfect square and therefore cannot be expressed in the form p/q, where p and q and non-negative integers and q = 0.

Hence, the given number is irrational.

Answer 2

Let us assume that √7 is a rational number.

So it t can be expressed in the form p/q where p,q are co-prime integers and q is not equal to zero

√7 = p/q

Here p and q are coprime numbers and q

Solving

√7 = p/q

On squaring both the side we get,

=> 7 = (p/q)2

=> 7q2 = p2…………..(1)

p2/7 = q2

So 7 divides p and p and p and q are multiple of 7.

⇒ p = 7m

⇒ p² = 49m² ……………..(2)

From equations (1) and (2), we get,

7q² = 49m²

⇒ q² = 7m²

⇒ q² is a multiple of 7 [Euclid's division lemma]

⇒ q is a multiple of 7 [Fundamental theorem of airthmetics]

Hence, p,q have a common factor 7. This contradicts our assumption that they are co-primes. Therefore, p/q is not a rational number

√7 is an irrational number.