Question

if ( x = sqrt{24} ) and ( y = sqrt{16} ), then what is the value of ( (x + y)(x - y) )?
(a) 2
(b) 4
(c) 6
(d) 8

Explanation:

Step1: Recall the formula

We know that \((x + y)(x - y)=x^{2}-y^{2}\) by the difference of squares formula.

Step2: Calculate \(x^{2}\) and \(y^{2}\)

Given \(x = \sqrt{24}\), then \(x^{2}=(\sqrt{24})^{2}=24\) (since \((\sqrt{a})^{2}=a\) for \(a\geq0\)).
Given \(y=\sqrt{16}\), then \(y^{2}=(\sqrt{16})^{2} = 16\) (since \((\sqrt{b})^{2}=b\) for \(b\geq0\)).

Step3: Substitute into the formula

\(x^{2}-y^{2}=24 - 16=8\)

Answer:

D. 8