Question

prove that root 2+ root 7 is irrational number​

Answer 1

Answer:

root 2+ root 7

root 2+root 7=a      (where a is an integer)

squaring both sides

(root 2+root 7)^2=(a)^2

(root 2)^2+(root 7)^+2(root 2)(root 7)=a^2

2+7+2 root 14=a^2

9+2 root 14 =a^2

2 root 14=a^2-9

root 14=a^2-9/2

since a is an integer therefore a^2-9/2 is also an integer and therefore root 14 is also an integer but integers are not rational numbers therefore root 2+root 7 is an irrational number.

proved.

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

Let us assume √2+√7 is rational

√2+√7=p/q

S.o.b.s

(√2+√7)^2={p/q}^2

..........

..........

√14=p^2-9q^2/2q^2

..,this is rational

So √14 is rational

This contradics the fact is it is irrational.

√2+√7 is irrational