Grade 9 Mathematics Radicals

1. WARM UP
ACTIVITY

2. SIMPLIFY THE FOLLOWING RADICAL
EXPRESSIONS
1) 25
2)
3
27
3) 18
4) 75
5)
3
32

3. ADDITION and
SUBTRACTION
of RADICAL
EXPRESSIONS
+
−

4. RADICALS Similar Radicals
3 2 and 4√2
6 𝑥 and −2 𝑥
𝑦
3
𝑥2𝑦 and 5𝑦
3
𝑥2𝑦
Dissimilar Radicals
2 and 15
6 𝑥 and 6𝑥
3 2 and 3 2

5. ADDING/SUBTRACTING
SIMILAR RADICALS
Combining like radicals is similar to combining
like terms.
Helpful Hint

6. MORE EXAMPLES!
III.
𝑦
3
𝑥2𝑦 + 5𝑦
3
𝑥2𝑦
= (𝑦 + 5𝑦)
3
𝑥2𝑦
= 6𝑦
3
𝑥2𝑦
II.
𝑚 − 7 𝑚
= (1 − 7) 𝑚
= −6 𝑚
1.
9 3 − 4 3
= (9 − 4) 3
= 5 3

7. TRY THIS!!!
III.
6𝑎
3
𝑐𝑑2 + 3𝑎
3
𝑐𝑑2
= (6𝑎 + 3𝑎)
3
𝑐𝑑2
= 9𝑎
3
𝑐𝑑2
II.
4 𝑛 + 8 𝑛
= (4 + 8) 𝑛
= 12 𝑚
1.
5 7 − 6 7
= (5 − 6) 7
= − 7

8. ADDING/SUBTRACTING
DISSIMILAR RADICALS
Factor the radicands using perfect
squares.
Product Property of Radicals
Simplify. Combine similar radicals

9. PERFORM THE INDICATED OPERATION
(𝟐𝟓)(𝟐) + (𝟏𝟔)(𝟐)
𝟓𝟎 + 𝟑𝟐
𝟗 𝟐
𝟓 𝟐 + 𝟒 𝟐
𝟐𝟓 𝟐 + 𝟏𝟔 𝟐
Factor the radicands using perfect
squares.
Product Property of Radicals
Simplify. Combine similar radicals

10. PERFORM THE INDICATED OPERATION
𝟔 𝟖 + 𝟐 𝟓𝟎 − 𝟐 𝟑𝟐
𝟔 𝟒 𝟐 + 𝟐 𝟐𝟓 𝟐 − 𝟐 𝟏𝟔 𝟐
𝟔 (𝟒)(𝟐) + 𝟐 (𝟐𝟓)(𝟐) − 𝟐 (𝟏𝟔)(𝟐)
𝟔(𝟐) 𝟐 + 𝟐(𝟓) 𝟐 − 𝟐(𝟒) 𝟐
𝟏𝟐 𝟐 + 𝟏𝟎 𝟐 − 𝟖 𝟐
(𝟏𝟐 + 𝟏𝟎 − 𝟖) 𝟐
𝟏𝟒 𝟐

11. TRY THIS!!!

12. APPLICATION:
Find the perimeter of a rectangular garden whose
length is 3 𝑏 inches and whose width is 2 𝑏 inches.
Give your answer as a radical expression in simplest
form.
The perimeter is𝟏𝟎 𝟓in.
𝑷 = 𝟐(𝑳 + 𝑾)

13. Find the perimeter of the triangular
roof. Give the answer as a radical
expression in simplest form.
𝑷 = 𝑺𝟏 + 𝑺𝟐 + 𝑺𝟑
Write an expression for perimeter.
Factor 20 using a perfect square.
Product Property of Square Roots.
Simplify.
Combine like radicals.

14. EVALUATION: ADD OR SUBTRACT
1) 8 6 + 22 6
2) 2 − 4 2
3) 11 𝑎𝑏 − 5 𝑎𝑏 + 3 𝑎𝑏
4) 2 3 + 4 12
5) 45𝑥 − 20𝑥 + 4 5𝑥

15. ASSIGNMENT: FIND THE PERIMETER OF THE
TRAPEZOID. GIVE THE ANSWER AS A RADICAL
EXPRESSION IN SIMPLEST FORM.