Adding and Subtracting Radicals

Question 1

Which of the following are like radicals? Check all of the boxes that apply.

Revolt · Accepted Answer

A: ; B: ; D: ; F:

Question 2

Which is a like radical to after simplifying?

Revolt · Accepted Answer

D:

Question 3

Which expression equals ?

Revolt · Accepted Answer

C:

Question 4

Find the difference:

Revolt · Accepted Answer

B:

Question 5

Simplify the following expression completely, where x 0.

Revolt · Accepted Answer

B:

Question 6

What is the student’s error?

Revolt · Accepted Answer

D: The student incorrectly simplified .

Question 7

Given that is it ever possible to have Explain.

Revolt · Accepted Answer

Yes, it is possible for 
𝑎
+
𝑏
=
𝑎
+
𝑏
a
	​

+
b
	​

=
a+b
	​

, but only in special cases. This happens if either 
𝑎
=
0
a=0 or 
𝑏
=
0
b=0, because the square root of 0 is 0. For example, if 
𝑎
=
0
a=0, then 
0
+
𝑏
=
0
+
𝑏
=
𝑏
=
0
+
𝑏
0
	​

+
b
	​

=0+
b
	​

=
b
	​

=
0+b
	​

. Similarly, if 
𝑏
=
0
b=0, the equation also works. In all other cases where both 
𝑎
a and 
𝑏
b are positive, the sum of the square roots is greater than the square root of the sum.

Question 8

Which of the following did you include in your response?

Revolt · Accepted Answer

A: Yes, it is possible to have the sum of square roots equal the square root of the sum of the radicands.; B: If either a or b equals zero, then the sums would be the same.; C: Since the square root of 0 is 0, adding it to a given radical would not change the radical. Also, adding zero to the radicand would not change its value.

Question 9

What is the radical part of both and when the expressions are simplified?

Revolt · Accepted Answer

A:

Question 10

Find the sum .

Revolt · Accepted Answer

A:

Adding and Subtracting Radicals Answers

More from this Course

TRY EDGENUITY HACKS