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Remember, to add or subtract radicals, there must be “like” terms in the problem.

Let’s now work the following practice problem.

5√8 + 6√25 + 7√98
5√8 = 5√4 • 2 = 5 • 2√2 = 10√2
6√25 = 6 • 5 = 30
7√98 = 7√49 • 2 = 7 • 7√2 = 49√2
10√2 + 49√2 = 59√2
Solution: 59√2 + 30

Note that “30” is not a like number to 59√2 so they are NOT added.

1.
2√3a3 + 5a√3a =
7a√3a
7a√3a2
7a2√3a
7a2√3a2
2√3a3 + 5a√3a
2√a2 • 3a + 5a√3a
2>a√3a + 5a√3a = 7a√3a
Solution: 7a√3a
Answer (a) is the correct solution
2.
2√24y - 2√54y =
10√6y
-2√6y
2√6y
-10√6y
2√24y - 2√54y
2√24y = 2√4 • 6 • y = 2 • 2√6y = 4√6y
2√54y = 2√9 • 6 • y = 2 • 3√6y = 6√6y
4√6y - 6√6y = -2√6y
Solution: -2√6y
Answer (b) is the correct solution
3.
√900 + √400 + √2500 + √1600 =
10√140
140
√140
10√90 + 40 + 250 + 160
√900 + √400 + √2500 + √1600
√900 = √100 • 9 = 10√9 = 10 • 3 = 30
√400 = √100 • 4 = 10√4 = 10 • 2 = 20
√2500 = √100 • 25 = 10√25 = 10 • 5 = 50
√1600 = √100 • 16 = 10√16 = 10 • 5 = 40
30 + 20 + 50 + 40 = 140
Solution: 140
Answer (b) is the correct solution
4.
3√18 + 3√12 + 3√18 =
6√18 + 6√3
18√2 + 6√3
6√18 + 3√12
18√2 + 12√3
3√18 + 3√12 + 3√18
3√18 + 3√18 = 6√18
6√18 = 6√9 • 2 = 6 • 3√2 = 18√2
3√12 = 3√4 • 3 = 3 • 2√3 = 6√3
18√2 + 6√3
Solution: 18√2 + 6√3
Answer (b) is the correct solution
5.
2√20 + √20 + 3√20 - 2√45 =
-6√5
18√5
-√5
6√5
2√20 + √20 + 3√20 - 2√45
2√20 + √20 + 3√20 = 6√20
6√20 - 2√45
6√20 = 6√4 • 5 = 6 • 2√5 = 12√5
2√45 = 2√9 • 5 = 2 • 3√5 = 6√5
12√5 - 6√5 = 6√5
Solution: 6√5
Answer (d) is the correct solution
6.
√5a2 + a√45 =
3a√52
4a√52
3a√5
4a√5
√5a2 + a√45
√5 (aa) = a√5
a√45 = a√9 • 5 (as 9 is a perfect square of 3, the 3 goes to the left of the √ symbol)
a√9 • 5 = 3a√5 We now have:
a√5 + 3a√5 = 4a√5
Solution: 4a√5
Answer (d) is the correct solution
7.
-√6 x - √54x =
-3√6x
2√6x
-4√6x
4√6x
-√6x - √54x
√54x = √9 • 6 • x = 3√6x
-√6x - 3√6x = -4√6x
Solution: -4√6x
Answer (c) is the correct solution
8.
2√18 - 2√12 + 2√18 =
12√2 - 4√3
8√9 - 6√4
7√2 - 4√3
12√2 + 4√3
2√18 - 2√12 + 2√18
2√18 + 2√18 = 4√18
4√18 - 2√12
4√18 = 4√9 • 2 = 4 • 3√2 = 12√2
2√12 = 2√4 • 3 = 2 • 2√3 = 4√3
12√2 - 4√3
Solution: 12√2 - 4√3
Answer (a) is the correct solution
9.
2√5x + 5√5x - 2√5x =
7√5x
-2√5x
5√5x
5√5x3
2√5x + 5√5x - 2√5x
2√5x - 2√5x = 0
5√5x + 0 = 5√5x
Solution: 5√5x
Answer (c) is the correct solution
10.
√32 + 9√2 + √18 =
16√2
16√23
11√2
-16√23
√32 + 9√2 + √18
√32 = √16 • 2 = 4√2
√18 = √9 • 2 = 3√2
4√2 + 9√2 + 3√2 = 16√2
Solution: 16√2
Answer (a) is the correct solution
Author:  Christine G. Broome