102 LearnersLast updated on August 30, 2025
Subtraction of Square Roots
The mathematical operation of finding the difference between two square roots involves the subtraction of square roots. This operation helps simplify expressions and solve problems involving square roots.
What is Subtraction of Square Roots?
Subtracting square roots involves simplifying the difference between two or more square root terms.
It requires ensuring that the square roots have the same radicand (the number inside the square root).
If the radicands are identical, you can subtract their coefficients.
Components involved in the subtraction of square roots include:
Radicands: These are the numbers under the square root symbol.
Coefficients: These are the numbers in front of the square root symbol.
How to do Subtraction of Square Roots?
When subtracting square roots, students should follow these rules:
Check for like radicands: Only square roots with identical radicands can be subtracted from one another.
Combine coefficients: Subtract the coefficients of like square roots.
Simplify result: If possible, simplify the resulting square root expression further.
Methods to do Subtraction of Square Roots
The following are methods for subtracting square roots:
Method 1: Direct Subtraction
For direct subtraction of square roots, follow these steps:
Step 1: Ensure the radicands are the same.
Step 2: Subtract the coefficients of the square roots.
Step 3: Simplify the expression if possible.
Example: Subtract √18 from 3√18
Step 1: Check radicands: both are √18.
Step 2: Subtract coefficients: 3 - 1 = 2.
Answer: 2√18
Method 2: Simplifying First Sometimes, it's easier to simplify square roots before subtracting:
Example: Subtract √50 from 5√2
Solution: Simplify √50 to 5√2, then subtract. 5√2 - 5√2 = 0
Properties of Subtraction of Square Roots
Subtraction of square roots has characteristic properties:
Subtraction is not commutative In subtraction, changing the order of terms changes the result, i.e., A - B ≠ B - A
Subtraction is not associative Regrouping changes the result: (A - B) - C ≠ A - (B - C)
Subtracting zero from an expression leaves the expression unchanged
Subtracting zero from any expression results in the same expression: A - 0 = A
Tips and Tricks for Subtraction of Square Roots
Tips and tricks are useful for efficiently dealing with the subtraction of square roots. Some helpful tips are:
Tip 1: Make sure radicands are the same before subtracting coefficients.
Tip 2: Simplify square roots whenever possible to make subtraction easier.
Tip 3: Use the properties of square roots to simplify expressions before subtraction.
Ignoring unlike radicands
Ensure that the radicands are identical before subtracting coefficients. Subtracting square roots with different radicands leads to errors.
Mistake 1
Incorrect simplification
Always simplify square roots correctly. Failing to do so can complicate the subtraction process.
Mistake 2
Forgetting to simplify the final result
After subtracting, always check if the result can be simplified further.
Mistake 3
Overlooking the zero coefficient
When subtracting identical square roots, remember that the result is zero, not a simplified square root.
Mistake 4
Misidentifying like terms
Only terms with the same radicands can be subtracted; misidentifying them leads to incorrect results.
Mistake 5
Examples of Subtraction of Square Roots
Subtract √12 from 5√12
4√12
Problem 1
Check radicands: both are √12. Subtract coefficients: 5 - 1 = 4 Result: 4√12
Subtract √45 from 2√45
Explanation
√45
Problem 2
Check radicands: both are √45. Subtract coefficients: 2 - 1 = 1 Result: √45
Subtract 3√7 from 7√7
Explanation
4√7
Problem 3
Both terms have the radicand √7. Subtract coefficients: 7 - 3 = 4 Result: 4√7
Subtract 4√3 from 9√3
Explanation
5√3
Problem 4
Both terms have the radicand √3. Subtract coefficients: 9 - 4 = 5 Result: 5√3
Subtract 2√11 from 6√11
Explanation
4√11
No, only square roots with the same radicands can be subtracted.
1.Is subtraction of square roots commutative?
2.What are like radicands?
3.What is the first step in subtracting square roots?
4.What is the best method for subtracting square roots?
5.How can children in Canada use numbers in everyday life to understand Subtraction of Square Roots?
6.What are some fun ways kids in Canada can practice Subtraction of Square Roots with numbers?
7.What role do numbers and Subtraction of Square Roots play in helping children in Canada develop problem-solving skills?
8.How can families in Canada create number-rich environments to improve Subtraction of Square Roots skills?
Common Mistakes and How to Avoid Them in Subtraction of Square Roots
Subtraction of square roots can be challenging and often leads to common mistakes. Being aware of these errors can help students avoid them.
About BrightChamps in Canada
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
