Combining Like Radicals
Master combining like radicals in Grade 9 math — Explanation Once you’ve found your 'radical twins' (like radicals), combining them is simple! Part of Rational Expressions and Radicals for Grade 9.
Key Concepts
Property To combine like radicals, add or subtract their coefficients, just like with like terms: $a\sqrt{x} + b\sqrt{x} = (a+b)\sqrt{x}$.
Explanation Once you’ve found your 'radical twins' (like radicals), combining them is simple! Just add or subtract the numbers in front, called coefficients, and keep the radical part the same. This works exactly like combining variables, such as $2x + 4x = 6x$. The radical is treated just like the variable part of a term.
Examples $2\sqrt{7} + 4\sqrt{7} = (2+4)\sqrt{7} = 6\sqrt{7}$ $4\sqrt{xy} 6\sqrt{xy} = (4 6)\sqrt{xy} = 2\sqrt{xy}$ $10\sqrt{3b} 2\sqrt{3b} = (10 2)\sqrt{3b} = 8\sqrt{3b}$.
Common Questions
What is 'Combining Like Radicals' in Grade 9 math?
Explanation Once you’ve found your 'radical twins' (like radicals), combining them is simple! Just add or subtract the numbers in front, called coefficients, and keep the radical part the same.
How do you solve problems involving 'Combining Like Radicals'?
Just add or subtract the numbers in front, called coefficients, and keep the radical part the same. This works exactly like combining variables, such as $2x + 4x = 6x$.
Why is 'Combining Like Radicals' an important Grade 9 math skill?
You can only combine radicals when the radicand is already the same.. Remember, you can't add an apple and an orange to get two 'apple-oranges'!.