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

1.	Show that 7 − √5 is irrational, give that √5 is irrational.
Answer» Let us assume, to the contrary that 7 − √5 is irrational 7 − √5 = p/q, Where p & q are co-prime and q ≠ 0 =√5 = 7q-p/q 7q - p/q is rational = √5 is rational which is a contradiction Hence 7 − √5 is irrational

Answer»

Let us assume, to the contrary that 7 − √5 is irrational

7 − √5 = p/q, Where p & q are co-prime and q ≠ 0 =√5 = 7q-p/q

7q - p/q is rational = √5 is rational which is a contradiction

Hence 7 − √5 is irrational

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

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