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$Pre-Algebra - Advanced Adding and Subtracting Radicals$

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Pre-Algebra - Advanced Adding and Subtracting Radicals

This Math quiz is called 'Pre-Algebra - Advanced Adding and Subtracting Radicals' and it has been written by teachers to help you if you are studying the subject at middle school. Playing educational quizzes is a fabulous way to learn if you are in the 6th, 7th or 8th grade - aged 11 to 14.

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If you have taken the Simple Adding and Subtracting Radicals quiz, that quiz will be a good foundation for tackling this advanced adding and subtracting of radicals. Here we will mostly be adding and subtracting multiple radicals.

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

1 .

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

2 .

√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

3 .

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

4 .

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

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 .

√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

7 .

√5a² + a√45 =

3a√5²

4a√5²

3a√5

4a√5

√5a² + a√45
√5 (a • a) = 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

8 .

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

9 .

2√5x + 5√5x - 2√5x =

7√5x

-2√5x

5√5x

5√5x³