Question

Assertion: Rationalising factor of `5 + 2sqrt(3)` is `5 - 2sqrt(3)`.

Reason: If the product of 2 irrational numbers is rational then each one is the rationalising factor of the other.

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 (A):

The rationalising factor of `5 + 2sqrt(3)` is `5 - 2sqrt(3)`.

• To rationalize, we multiply by the conjugate.
• Conjugate of `5 + 2sqrt(3)` is `5 - 2sqrt(3)`
• Their product `(5 + 2sqrt(3))(5 - 2sqrt(3)) = 25 - (2sqrt(3))^2 = 25 - 12 = 13` (rational)

Reason (R):

If the product of 2 irrational numbers is rational then each one is the rationalising factor of the other.

• This is the definition of rationalising factor.
• Example: `sqrt(3)` and `-sqrt(3)` multiply to –3, a rational number. Each is the rationalising factor of the other.