Math, asked by VinitMalapati942, 1 year ago

Prove that 3+ root 5 is irrational ​

Answers

Answered by ShahzebSheikh
2

Here,

Let us assume that 3 + √5 is a rational number.

Then we can find co prime numbers a and b such that 3 + √5 = a/b

                         ⇒ √5 = a/b - 3

                         ⇒ √5 = a-3b/b

                 

∴ a and b are integers , a-3b/b is a rational.

But we know that √5 is an irrational number.

Our assumption is wrong as irrational number ≠ rational number. This contradiction is due to our assumption that 3 + √5 is a rational number. rational number.

                     

So, 3 + √5 is an irrational number.

Answered by Anonymous
0

Answer:

Step-by-step explanation:

Let

3 + √5 is a rational number.

we can find co prime numbers p and q  of  3+ root 5

3 + root 5 = p/q    [ where p and q are integer , q ≠ 0 and q and p are co - prime number ]

root 5 = p/q -3

root 5 = p - 3q/p

we know that p/q is a rational number.

.°. √5 is also a irrational number.

This contradicts our assumption.

.°. 3 +√5 is an irrational number.

∴ p and q are integer

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