Question

show that 7 root 2 is a irrational number

Answer 1

Answer:

show that 7 root 2 is an irrational number

let 7 root 2 be rational no.

7root 2= p upon q

root 2= p upon 7q

now p upon q is a rational no.

then p upon 7q is also a rational no.

then root 2 is also rational no.

but it contradicts the fact that root 2 is irrational no.

root 2 is not equal to p upon 7 q

our assumption is wrong.

hence 7 root 2 is an irrational no.

Answer 2

7√2 is an irrational number.

GIVEN

A number 7√2

TO FIND

To show that the given number is an irrational number.

SOLUTION

We can simply solve the above problem as follows;

We are given a number, 7√2.

We have to proof that 7√2 is an irrational number.

Let us assume that 7√2 is a rational number.

We know that a rational number that can be written in the form p/q, where q≠ zero.

If 7√2 is a rational number,

7√2 = p/q

Bringing 7 at RHS

√2 = p/7q

We know that √2 is an irrational number.

Since, LHS ≠ RHS

Therefore, Our assumption is wrong.

Hence,

7√2 is an irrational number.

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