1.

Prove that 8- root 2 is irrational

Answer»

<P>Answer:

Step-by-step EXPLANATION:

√2 is an irrational number

Suppose it can be WRITTEN in the form of p/q, and q is not equal to zero.

When p and q are RELATIVE prime numbers

√2= p/q~~eq(1)

Where p and q are relative prime number

TAKING square on both sides of eq(1)

2=p2/q2

Splitting q2 in two terms

2=p2/q.q

Now, taking one q on other side

2q=p2/q~~eq(2)

Since p and q being relative prime number, q cannot divide p and p2.

As l.h.s of eq(2) is an integer i.e; na

Hence, l.h.s of eq(2) is not equal to r.h.s.

Hence, out assumption is wrong.

So, it is proved that √2 is an irrational number.


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