Test Questions for Rationalizing Monomial Denominators

📚 Quick Study Guide

• 🔍 Rationalizing the Denominator: This means eliminating any radical expressions (like square roots) from the denominator of a fraction.
• 💡 Monomial Denominator: A monomial denominator is a single term, such as $3\sqrt{x}$ or $5y^2$.
• 📝 Key Principle: Multiply both the numerator and denominator by a suitable expression that will eliminate the radical in the denominator.
• ➗ Fraction Rule: Remember, multiplying the numerator and denominator by the same non-zero expression doesn't change the value of the fraction.
• ➗ Square Root Rule: $\sqrt{a} \cdot \sqrt{a} = a$
• ➮ Example: To rationalize $\frac{1}{\sqrt{2}}$, multiply both numerator and denominator by $\sqrt{2}$ to get $\frac{\sqrt{2}}{2}$.

Practice Quiz

1. What is the first step in rationalizing the denominator of $\frac{4}{\sqrt{5}}$?
   1. Multiply the numerator and denominator by 4.
   2. Multiply the numerator and denominator by $\sqrt{5}$.
   3. Square the entire fraction.
   4. Simplify the numerator.
2. Rationalize the denominator of $\frac{2}{\sqrt{3}}$. What is the result?
   1. $\frac{2\sqrt{3}}{9}$
   2. $\frac{\sqrt{3}}{3}$
   3. $\frac{2\sqrt{3}}{3}$
   4. $\frac{4\sqrt{3}}{3}$
3. Rationalize the denominator of $\frac{5}{\sqrt{7}}$.
   1. $\frac{5\sqrt{7}}{49}$
   2. $\frac{\sqrt{7}}{5}$
   3. $\frac{5\sqrt{7}}{7}$
   4. $\frac{7\sqrt{5}}{5}$
4. Simplify: $\frac{10}{\sqrt{2}}$
   1. $5\sqrt{2}$
   2. $2\sqrt{5}$
   3. $10\sqrt{2}$
   4. $\sqrt{5}$
5. What is the rationalized form of $\frac{3}{\sqrt{11}}$?
   1. $\frac{3\sqrt{11}}{121}$
   2. $\frac{\sqrt{11}}{3}$
   3. $\frac{3\sqrt{11}}{11}$
   4. $\frac{11\sqrt{3}}{3}$
6. Rationalize the denominator of $\frac{1}{\sqrt{13}}$
   1. $\frac{13}{\sqrt{13}}$
   2. $\sqrt{13}$
   3. $\frac{\sqrt{13}}{13}$
   4. $\frac{13\sqrt{13}}{13}$
7. Simplify: $\frac{8}{\sqrt{8}}$
   1. $2\sqrt{2}$
   2. $\sqrt{8}$
   3. $4\sqrt{2}$
   4. $\sqrt{2}$