Question

1. what does it mean to rationalize the denominator?

Explanation:

Rationalizing the denominator means eliminating any radicals (like square roots, cube roots) from the denominator of a fraction. This is done by multiplying both the numerator and the denominator by an appropriate expression. For example, if the denominator is \(\sqrt{a}\), we multiply numerator and denominator by \(\sqrt{a}\) so that the denominator becomes \(a\) (since \(\sqrt{a}\times\sqrt{a}=a\)). If the denominator is of the form \(a +\sqrt{b}\), we use the conjugate \(a-\sqrt{b}\) and multiply numerator and denominator by \(a - \sqrt{b}\) (using the formula \((x + y)(x - y)=x^{2}-y^{2}\)).

Answer:

Rationalizing the denominator is the process of eliminating radicals from the denominator of a fraction by multiplying the numerator and denominator by an appropriate expression.