Question

(ii) Every real number 15
2. Are the square roots of all positive integers irrational? If not, give an example of the
square root of a number that is a rational number.​

Answer 1

Explanation:

No, square roots of all positive integers are not irrational.

A few such examples are : 25, 36, 4 ..

√25 = √( 5 × 5 ) = √5² = 5

( which is rational )

√36 = √(6 × 6) = √6² = 6

( which is rational )

√4 = √(2 × 2) = √2² =

2 ( which is rational )

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Square roots of the positive integers that are not perfect square are irrational. The same thing goes for cube roots, forth root, fifth root and all.

Examples are :

√21

here 21 is not a perfect square, so √21 is irrational

√43

here 43 is not a perfect square, so √43 is irrational

Answer 2

No, the square roots of all positive integers are not irrational.

For example,

√4 = 2 is rational

√9 = 3 is rational.

Hence, the square roots of positive integers 4 and 9 are not irrational. (2 and 3, respectively)