Mathematics 2021 JAMB Past Questions - Question 7: Simplify 2√2 - √3 / √2 + √2

Correct Answer

B

Explanation

To simplify the expression (2√2 - √3) / (√2 + √2), we can follow these steps:First, let's simplify the numerator (2√2 - √3):The terms in the numerator have different radicals, so we cannot combine them directly. We'll leave them as they are for now.Next, let's simplify the denominator (√2 + √2):√2 + √2 can be simplified as 2√2.Now, let's substitute the simplified numerator and denominator back into the expression:(2√2 - √3) / (√2 + √2) = (2√2 - √3) / 2√2Since the numerator and denominator have a common factor of 2√2, we can cancel them out:(2√2 - √3) / 2√2 = (2√2 - √3) / (2√2) = (2√2) / (2√2) - (√3) / (2√2) = 1 - (√3) / (2√2)To simplify further, we can rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator, which is √2:1 - (√3) / (2√2) = (1 - (√3) / (2√2)) * (√2 / √2) = (√2 - √6) / (2 * 2) = (√2 - √6) / 4Therefore, the simplified form of the expression (2√2 - √3) / (√2 + √2) is (√2 - √6) / 4.