Question

State ,give reason, whether the number is rational or irrational :
5√6
-√7

Answer 1

Answer:

Irrational

Step-by-step explanation:

To prove:

Let us assume on the contrary that 5√6-√7 is a rational number. Then there exist co-prime integers a and b such that

5√6-√7=a/b

or a/b+√7=5√6

and by squaring the equation

i. e. (a/b+√7)^2=(√5)^2

or a^2/b^2+2a.√7/b+7=150

a^2/b^2-143=-2a√7/b

or (a^2-143b^2)/-2ab=√7

Since, a, b are integers and

(a^2-143b^2)/-2ab is a rational no.

√7 is also rational

This contradicts the fact that √2 is an irrational.so our assumption is wrong

Hence 5√6-√7is irrational.

Answer 2

Answer:

YOUR CORRECT ANSWER IS

IRRATIONAL