Math: Middle School: Grades 6, 7 and 8 Quiz - Pre-Algebra - Advanced Adding and Subtracting Radicals (Answers)
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.
It costs only $12.50 per month to play this quiz and over 3,500 others that help you with your school work. You can subscribe on the page at Join Us
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.
[readmore]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.
[/readmore]
|
|
||||||||||||||||||||||||
|
|
||||||||||||||||||||||||
|
|
||||||||||||||||||||||||
|
|
||||||||||||||||||||||||
|
|
|
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 |
||||||||||||||||||||||||
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 |
-√6x - √54x
√54x = √9 • 6 • x = 3√6x -√6x - 3√6x = -4√6x Solution: -4√6x Answer (c) is the correct solution |
||||||||||||||||||||||||
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 |
√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 |
||||||||||||||||||||||||
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√5x + 5√5x - 2√5x
2√5x - 2√5x = 0 5√5x + 0 = 5√5x Solution: 5√5x Answer (c) is the correct solution |
||||||||||||||||||||||||
√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 |
√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√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