Question

prove that √5 is an irrational number​

Answer 1

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$\huge\bold\red{Answer}$

Let assume that √5 is an irrational number.

∴ It can be expressed in the form p/q where p,q are co-prime integers.

⇒√5=p/q

⇒√5=p/q

⇒5=p²/q²_______(1) {Squaring both the sides}

⇒p² is a multiple of 5.

⇒p is also a multiple of 5.

⇒p=5m

⇒p=5m

⇒p²=25m² __________ (2)

From equations (1) and (2),

5q²=25m²

5q²=25m²⇒q²=5m²

⇒q² is a multiple of 5.

⇒q is a multiple of 5.

Therefore, p/q is not a rational number. This proves that √5 is an irrational number.

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Answer 2

Answer:

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Step-by-step explanation:

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