Question

Assertion: `(sqrt(6) + sqrt(24))^2` is a rational number.

Reason: Product of 2 irrational numbers can be rational or irrational.

Options

• Both A and R are true and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

Both A and R are true and R is the correct reason for A.

Explanation:

Assertion:

`(sqrt(6) + sqrt(24))^2`

First, simplify `sqrt(24)`:

`sqrt(24) = sqrt(4 * 6) = 2sqrt(6)`

So, `(sqrt(6) + sqrt(24))^2 = (sqrt(6) + 2sqrt(6))^2`

= `(3sqrt(6))^2`

= `9 * 6`

= 54

54 is a rational number.

So the Assertion is true.

Reason:

Product of 2 irrational numbers can be rational or irrational.

Example:

• `sqrt(2) * sqrt(2) = 2` → rational
• `sqrt(2) * sqrt(3) = sqrt(6)` → irrational

This is a true statement.