Question

prove √3/5 is irrational number
class 10​

Answer 1

Step-by-step explanation:

3 + 5 = p q , where p and q are the integers and q ≠0. Since p , q and 3 are integers. So, p - 3 q q is a rational number. ... Hence, is an irrational number

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Answer 2

Given :-

• A Irrational Number √3/5 .

To Prove :-

• It is a Irrational Number.

Proof :-

Firstly we must know that ,

• Sum of rational number and a Irrational number is Irrational.
• Difference of rational number and a Irrational number is Irrational.
• Multiplication of rational number and a Irrational number is Irrational.
• Division of rational number and a Irrational number is Irrational.

Let's try to Prove √3 as Irrational Number.

On the contrary let us assume that √3 is a a rational number so it can be expressed in the form of p by q where p and q are integers and q is not equal to zero , also HCF of p and q is one.

⇒ √3 = p/q .

⇒ (√3)² =(p/q)².

⇒ 3 = p²/q².

⇒ 3q²=p².

This implies that 3 is a factor of p² .

So it will divide p also .

Let p = 3k .............(i)

⇒ 3q²=(3k)².

⇒ 3q²=9k².

⇒q²=9k²/3.

⇒q²=3k².

This implies that 3 is a factor of q² .

So it will divide q also .

This contradicts our assumption that p and q are co-primes . Hence our assumption was wrong .

√3 is a Irrational Number.

So , now 5 is a Rational number . And √3 is Irrational number . And we know that division of rational number and a Irrational Number is always Irrational .

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