Rationalize and simplify.
5 / (3 + √2)
Show answer & explanation
Correct answer: C
Explanation
Given:
5 / (3 + √2)
According to the formula:
To rationalize (a / (b + c)), we multiply both the numerator and the denominator by (b − c).
5 / (3 + √2) × (3 − √2) / (3 − √2)
= 5(3 − √2) / ((3 + √2)(3 − √2))
= 5(3 − √2) / (9 − 2)
= 5(3 − √2) / 7
= (15 − 5√2) / 7