Question

Which of the following is the rationalized form of the denominator in the expression 2/(√3 - 1)?

A) √3 + 1
B) √3 - 1
C) 2√3 - 2
D) 2√3 + 2

Answer 1

The rationalized form of the denominator for the expression 2/(√3 - 1) is √3 + 1, which is achieved by multiplying both the numerator and the denominator by the conjugate of the denominator (√3 + 1).

Step-by-step explanation:

The rationalized form of the denominator in the expression 2/(√3 - 1) is accomplished by multiplying the numerator and denominator by the conjugate of the denominator. The conjugate of √3 - 1 is √3 + 1.

Multiplying both the numerator and denominator by the conjugate, we get:

• (2 * (√3 + 1)) / ((√3 - 1) * (√3 + 1))
• (2√3 + 2) / (3 - 1)
• (2√3 + 2) / 2
• √3 + 1

Thus, the rationalized form of the denominator in the given expression is √3 + 1.