Question

Show that 8+ 2* square root of 15 is an irrational no

Answer 1

Let us assume (8+2√15) is

a rational.

8+2√15 = a/b

where a,b are integers and

b≠0

=> 2√15 = a/b - 8

=> 2√15 = (a-8b)/b

=>√15 = (a-8b)/2b

Since , a,b are integers, (a-8b)/2b is a rational ,So, √15 is a

rational.

But , this contradicts that the

fact that √15 is irrational.

Therefore,

8+2√15 is an irrational.

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Answer 2

15.74596669 is the exact answer really i done this without calculator .