Question

prove that the following are irrational 7√5​

Answer 1

7√5 = 15.652475842...

This decimal expansion is non terminating and non recurring.

Therefore, 7√5 is an irrational number.

BECAUSE,

Decimal expansion of a number is non terminating and non recurring, is an Irrational number.

Hope it is helpful ✌️

Answer 2

let us assume √5 is rational no.

√5=a/b (where a and b are any

integer and b is not equal

0)

√5b=a

squaring both side

(√5b)^2 =(a)

5b^2 =a^2(a^2 is divided by 5 so a is also

divisible by 5)

b^2=a^2/5

therefore,

a=5c (where c is any integer)

√5b=5c

squaring both side

(√5b)^2=(5c)^2

5b^2=25c^2

b^2=5c^2

there a and b have at least 5as a commo n factor .so,our assumption is wrong and √5 is irrational.

assume 7√5 is rational

7√5=a/b(where a and b are integer and

b is not equal to 0)

√5=a/b+7/1

√5=a+7b/b = rational

but we above stated that √5 is irrational.So,our assumption is wrong and therefore.7√5is irrational