Example Card: Combining Like Radicals
Combine like radical expressions in Grade 9 Algebra by adding or subtracting their coefficients. Simplify each radical to identify matching radicands before combining.
Key Concepts
Adding radicals is just like combining like terms—if the core part matches, they mix. This first key idea, combining like radicals, is the foundation for everything else in this lesson.
Example Problem Simplify the expression $\frac{5\sqrt{3p}}{9} + \frac{2\sqrt{3p}}{9} \frac{6\sqrt{2q}}{9}$.
Step by Step 1. First, we identify the like radicals in the expression. The terms with $\sqrt{3p}$ are like radicals. $$ \frac{5\sqrt{3p}}{9} + \frac{2\sqrt{3p}}{9} \frac{6\sqrt{2q}}{9} $$ 2. We can combine the coefficients of the like radicals since they share a common denominator. $$ = \frac{(5+2)\sqrt{3p}}{9} \frac{6\sqrt{2q}}{9} $$ 3. The term with $\sqrt{2q}$ has a different radicand, so it is an unlike radical and cannot be combined further. $$ = \frac{7\sqrt{3p} 6\sqrt{2q}}{9} $$.
Common Questions
What is Example Card: Combining Like Radicals in Grade 9 Algebra?
Adding radicals is just like combining like terms—if the core part matches, they mix Mastering this concept builds a foundation for advanced algebra topics.
How do you approach Example Card: Combining Like Radicals problems step by step?
This first key idea, combining like radicals, is the foundation for everything else in this lesson Use this method consistently to avoid common errors.
What is a common mistake when studying Example Card: Combining Like Radicals?
First, we identify the like radicals in the expression Always check your work by substituting back into the original problem.