Question

Which of the following statements is true?

Both √5/8 and √4/9 are irrational
√5/8 is rational and √4/9 is irrational
√5/8 is irrational and √4/9 is rational
both √5/8 and √4/8 are rational

Answer 1

C - √5/8 is irrational and √4/9 is rational

Answer 2

`(√(5))/(8)` is irrational and
`(√(4))/(9)` is rational .

Explanation:

Given : Statements Both √5/8 and √4/9 are irrational

√5/8 is rational and √4/9 is irrational

√5/8 is irrational and √4/9 is rational

both √5/8 and √4/8 are rational.

To find : Which of the following statements is true.

Solution : We have given
`(√(5))/(8)` and
`(√(4))/(9)` .

Rational number : A number is rational if we can write it as a fraction where the numerator and denominator are both whole numbers.

Irrational number : an irrational number is any number that is not rational. It is a number that cannot be written as a ratio of two integers.

`√(5)` is not an integer so,
`(√(5))/(8)` is irrational number .

`√(4)` = 2 so, it is an integer then it is rational number.

Therefore,
`(√(5))/(8)` is irrational and
`(√(4))/(9)` √4/9 is rational .