Operations with Radicals
Radical expressions can be combined (added or subtracted) if they are like radicals – that is, they have the same index and radicand. To determine whether two radicals can be combined, you should first simplify each radical.
The rules for doing arithmetic with square roots are quite simple:
- Multiplication: “the product of square roots is the square root of the product”. When multiplying radicals, one must multiply the numbers OUTSIDE (O) the radicals AND then multiply the numbers INSIDE (I) the radicals.
- Division: “the quotient of square roots is the square root of the quotient”When dividing radicals, one must divide the numbers OUTSIDE (O) the radicals AND then divide the numbers INSIDE (I) the radicals.
Read the explanation below to learn more about operations with radicals.
Practice: Add, subtract, multiply and divide radical expressions in the following exercises.