In the following equations, find which variables `x ,\ y ,\ z` etc. represent rational or irrational numbers: `v^2=3\ ` (ii) `w^2=27` (iii) `t^2=0. 4`

Explanation

(i)`v^2=3` = Taking square root both the sides, we get ` v = (sqrt(3))`
Since, `(sqrt 3)` is not a perfect square root, so `v` is irrational number.
(ii) `w^2=27`
Taking square root both the sides, we get `w = 3(sqrt 3)`
We know that, the product of a rational and irrational is an irrational number. Therefore, `w` is an irrational number.
(iii) `t^2=0. 4`=Taking square root both the sides, we get `t `= `sqrt(4/10)`
` t = 2/ (sqrt10 )`
We know that, quotient of a rational and an irrational number is irrational number.
Therefore, t is an irrational number.