Identify the radical in the denominator.

Question

ScanSolve AI Tutor · Accepted Answer

let's correct the rationalization of the expression $\frac{-2 + \sqrt{21}}{\sqrt{21}}$ .

Identify the radical in the denominator.
The denominator is $\sqrt{21}$ . To rationalize it, we need to multiply both the numerator and the denominator by $\sqrt{21}$ .
Multiply the expression by $\frac{\sqrt{21}}{\sqrt{21}}$ .
$\frac{-2 + \sqrt{21}}{\sqrt{21}} \times \frac{\sqrt{21}}{\sqrt{21}}$
Distribute $\sqrt{21}$ to each term in the numerator and simplify the denominator.
$\frac{(-2)\sqrt{21} + (\sqrt{21})(\sqrt{21})}{(\sqrt{21})(\sqrt{21})}$
Simplify the terms in the numerator and denominator.
$\frac{-2\sqrt{21} + 21}{21}$
Rearrange the terms in the numerator for standard form.
$\frac{21 - 2\sqrt{21}}{21}$

Answer