Question

prove 8+4√12 is an irrational number​

Answer 1

Step-by-step explanation:

Let us assume to the contrary that 8+4√12 is an rational number,

now. 8+4√12= a/b (where a and b are coprimes and b is not = to Zero)

4√12 = a/b -8

√12 =a-8b/4b

as a-8b/4b is in p/q form so 8+4√12 is an rational number .

But we know that √12 is an irrational number.

Hence our assumption is wrong.

Thus 8+4√12 is an irrational number..

Answer 2

Answer:

8+4√2 is irritational no.

Step-by-step explanation:

let √2 is a rational no.

√2 be form in p/q

so √2 =p/q

squaring both side

(√2)²=(p/q)²

2p²=q²

p² is divisible by 2

hence p is also divisible by 2 ........(1

let 2r=q

squaring both side

: (2r)²=q²

hence q² is also divisible by 2

so q is also divisible by 2 ........(2

so we can say that by (1 and (2 the √2 can not form p/q so our assumption is wrong so √2 is an irrational number