Question

Rationalize the given denominator of √2 - 1.

a) √2 + 1
b) √2 - 1
c) √2 + 1/2
d) √2 - 1/2

Answer 1

To rationalize the denominator of √2 - 1, multiply by the conjugate √2 + 1. This process will result in a rationalized denominator, making √2 + 1 the correct answer.

Step-by-step explanation:

To rationalize the denominator of the expression √2 - 1, you should multiply both the numerator and the denominator by the conjugate of the denominator, which is √2 + 1. The conjugate is a binomial formed by changing the sign of the second term in the denominator. When multiplied, the result will only have rational numbers.

Here's the process in detail:

(√2 - 1)(√2 + 1) / (√2 - 1)(√2 + 1)
↓
= (√2² - 1²) / (rationalized denominator)
↓
= (2 - 1) / (rationalized denominator)
↓
= 1 / (rationalized denominator).

Solving this will show that √2 + 1 is the correct answer.