Question

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Prove that √5 is irrational?​

Answer 1

Problem statement: Prove that Root 5 is Irrational Number

Given: The number 5

Proof: On calculating the value of √5,  we get the value √5 = 2.23606797749979...As discussed above a decimal number that does not terminate after the decimal point is also an irrational number. The value obtained for the root of 5 does not terminate and keeps extending further after the decimal point. This satisfies the condition of √5 being an irrational number.  

Hence, √5 is an irrational number.  

The square root of 5 is commonly also called "root 5". The root of a number "n" is represented as √n. Thus, we define the root of a number as the number that on multiplication to itself gives the original number. For example, √5 on multiplication to itself gives the number 5. In order to prove that root 5 is an irrational number, we use different methods like the contradiction method and long division method.

Answer 2

Answer:

Prove That Root 5 is Irrational by Contradiction Method

Assuming if p was a prime number and p divides a2, then p divides a, where a is any positive integer. Hence, 5 is a factor of p2. This implies that 5 is a factor of p.

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