Question

Show that 7 − √5 is irrational, give that √5 is irrationa

Answer 1

Answer:

7-√5 is irrational number.

Step-by-step explanation:

As per given in thhe question that √5 is irrational.

So if we subtract any number form irrational then result is irrational.

Answer 2

Let 7 - √5 be a rational number Then It can be represented in the form of p/q where p and q are integers having common factor not other than 1 and q ≠ 0,

Given: √5 is irrational

7 - √5 = p/q

7 - p/q = √5

7q - p / q = √5

Since 7q - p and q are rational numbers and therefore √5 is a rational number also but this contradicts the fact that √5 is irrational. Because our assumption was wrong and 7 - √5 is irrational.