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WHAT IS A RADICAL? 
A RADICAL EXPRESSION OR RADICAL IS A 
TERM OR EXPRESSION THAT CONTAINS A 
SQUARE ROOT 
Addition 
Addition and subtraction of radicals involve the same 
concept in adding and 
subtracting integers or whole numbers.
Parts of a radical expression
Addition 
• -Simplify the radical 
expressions by finding the root 
of the radicand or factoring it 
out 
Simplify the terms. 
-If there is no square root, use 
prime factorization on the 
numbers.
Prime factorization 
The first few prime numbers are: 2, 3, 5, 7, 11, 13, and 17 
...
Addition 
• -Simplify the radical 
expressions by finding the root 
of the radicand or by factoring 
it out. 
-If there is no square root, use 
prime factorization on the 
numbers.
Addition 
- Simplify the terms. 
- -If the exponent is greater 
than or equal to the index, 
then it can be taken 
outside the radicand.
subtraction 
- Find the root of the radicand 
or factor it out. 
Do the same procedure in adding 
radicals. The only thing to change is 
the operation.
subtraction 
--If the exponent is 
greater than or equal 
to the index, then it 
can be taken outside 
the radicand. 
-simplify the terms.
REMEMBER! 
We can only combine like radicals. 
Don’t forget the index. The most common value of the 
index (root) is 2. but it can also be 3 or more. (cube, 
fourth root, etc)
Let’s try!
REMEMBER! 
• We can only combine like radicals. 
• Don’t forget the index. The most common value of the 
index (root) is 2. but it can also be 3 or more. (cube, fourth 
root, etc)

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Addition and Subtraction of Radicals

  • 1.
  • 2. WHAT IS A RADICAL? A RADICAL EXPRESSION OR RADICAL IS A TERM OR EXPRESSION THAT CONTAINS A SQUARE ROOT Addition Addition and subtraction of radicals involve the same concept in adding and subtracting integers or whole numbers.
  • 3. Parts of a radical expression
  • 4. Addition • -Simplify the radical expressions by finding the root of the radicand or factoring it out Simplify the terms. -If there is no square root, use prime factorization on the numbers.
  • 5. Prime factorization The first few prime numbers are: 2, 3, 5, 7, 11, 13, and 17 ...
  • 6. Addition • -Simplify the radical expressions by finding the root of the radicand or by factoring it out. -If there is no square root, use prime factorization on the numbers.
  • 7. Addition - Simplify the terms. - -If the exponent is greater than or equal to the index, then it can be taken outside the radicand.
  • 8. subtraction - Find the root of the radicand or factor it out. Do the same procedure in adding radicals. The only thing to change is the operation.
  • 9. subtraction --If the exponent is greater than or equal to the index, then it can be taken outside the radicand. -simplify the terms.
  • 10. REMEMBER! We can only combine like radicals. Don’t forget the index. The most common value of the index (root) is 2. but it can also be 3 or more. (cube, fourth root, etc)
  • 12. REMEMBER! • We can only combine like radicals. • Don’t forget the index. The most common value of the index (root) is 2. but it can also be 3 or more. (cube, fourth root, etc)