Question

proove that 3-root 5 is an irrational number​

Answer 1

Answer:

because it 9is not diviable by 2.

Answer 2

To prove :-3-√5 is irrational.

Proof:-

3+ √5

Let us assume 3+√5 be rational number.

Now,

3+√5 -3 (subtracting rational from rational )

now it's √5 which is irrational.

So, 3+√5 is irrational.

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√5 is irrational proof.

√5 = a ÷ b (a and b are co prime numbers)

=>b√5=a

Now, squaring on both sides. We get ,

=>5b² = a².........{1}

=>b²=a²÷5

Hence 5 devides a².

5 devides a also.

Now,

a =5c (here c is any integer)

Sq. on both sides

=>a²=25c²

=>5b²=25c² (from 1.)

=> b² =5c²

=>c²=b²÷5

Here 5 devides b²

and 5 devides b also,

=> a & b are Co prime numbers & 5 devide both of them .

Hence √5 is irrational number.

So proved.

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