Mathematics 2000 JAMB Past Questions - Question 3: 2√3 - √2/√3 + 2√2 = m+n√6; Find the values of m and n respectively

Correct Answer

B

Explanation

To find the values of m and n in the expression 2√3 - √2/√3 + 2√2 = m + n√6, we need to simplify the expression and compare it with the form m + n√6.Let's simplify the expression step by step:2√3 - √2/√3 + 2√2First, let's rationalize the denominator of the second term (√2/√3) by multiplying the numerator and denominator by √3:2√3 - (√2/√3) * (√3/√3) + 2√22√3 - (√2 * √3)/(√3 * √3) + 2√22√3 - √6/√9 + 2√22√3 - √6/3 + 2√2Now, let's combine like terms:(2√3 + 2√2) - (√6/3)Next, let's find a common denominator for the terms inside the parentheses:(2√3 * √3 + 2√2 * √3 - √6)/3Simplifying further:(2√9 + 2√6 - √6)/3(2 * 3 + 2√6 - √6)/3(6 + √6)/3Now, we can compare this expression with the form m + n√6:m + n√6 = (6 + √6)/3Comparing the coefficients, we can see that m = 6/3 = 2 and n = 1.Therefore, the values of m and n are 2 and 1, respectively.To simplify the expression 2√3 - √2/√3 + 2√2, we can combine like terms. First, let's simplify the expression √2/√3. To do this, we need to rationalize the denominator by multiplying both the numerator and denominator by √3:(√2/√3) * (√3/√3) = (√6)/3Now, let's substitute this back into the original expression:2√3 - (√6)/3 + 2√2Next, let's combine the terms with √3 and √2:2√3 + 2√2 - (√6)/3To simplify further, we can find a common denominator for the terms with √3 and √2, which is 3:(2√3 * 3 + 2√2 * 3 - (√6))/3(6√3 + 6√2 - (√6))/3Now, we can rewrite this expression as m + n√6:m = (6√3 - (√6))/3n = 6Therefore, the values of m and n are:m =  6√3 - (√6)/3 n = 6m = -2, n = 1