Rationalize the Denominator
Understand rationalize the denominator in Grade 9 math — Explanation It’s considered bad manners in math to leave a radical in the basement (the denominator)!
Key Concepts
Property To rationalize a denominator means to use a method which removes radicals from the denominator of a fraction. Explanation It’s considered bad manners in math to leave a radical in the basement (the denominator)! To clean it up, we cleverly multiply by a form of 1, like $$ \frac{\sqrt{3}}{\sqrt{3}} $$, which kicks the radical out of the denominator without changing the fraction’s value. Examples $$ \frac{\sqrt{7}}{\sqrt{2}} = \frac{\sqrt{7}}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{14}}{2} $$ $$ \sqrt{\frac{5}{a}} = \frac{\sqrt{5}}{\sqrt{a}} \cdot \frac{\sqrt{a}}{\sqrt{a}} = \frac{\sqrt{5a}}{a} $$.
Common Questions
What is 'Rationalize the Denominator' in Grade 9 math?
Explanation It’s considered bad manners in math to leave a radical in the basement (the denominator)! To clean it up, we cleverly multiply by a form of 1, like $$ \frac{\sqrt{3}}{\sqrt{3}} $$, which kicks the radical out of the denominator without changing the fraction’s value.
How do you solve problems involving 'Rationalize the Denominator'?
To clean it up, we cleverly multiply by a form of 1, like $$ \frac{\sqrt{3}}{\sqrt{3}} $$, which kicks the radical out of the denominator without changing the fraction’s value. In math, it's a standard rule not to leave a square root (a radical) in the bottom part of a fraction (the denominator).
Why is 'Rationalize the Denominator' an important Grade 9 math skill?
Remember, it only turns the specific term it's attached to into 1.. In the problem above, only $(10y^5z^2)$ becomes 1, not the $7x^3$.