Square Root Subtraction
How to Subtract Square Roots
Square root subtraction follows the same rule as addition — you can only subtract like radicals (same number under the root).
Rule: Like radicals can be subtracted
a√x − b√x = (a − b)√x
Example: 7√3 − 2√3 = (7−2)√3 = 5√3
Example: 9√5 − 4√5 = 5√5
Simplify unlike radicals first
Example: √18 − √2 = 3√2 − √2 = 2√2 (because √18 = √(9×2) = 3√2)
Cannot be subtracted
√5 − √3 ≠ √2 (this is WRONG)
Unlike radicals that cannot be simplified to matching forms must be left as-is or evaluated numerically.