Question

Jordan simplified the expression
4
√
3
+
5
√
6
(
8
√
2
)
with the steps shown but made an error.



Step 1:
4
√
3
+
5
√
6
(
8
√
2
)

Step 2:
4
√
3
+
40
√
12

Step 3:
4
√
3
+
80
√
3

Step 4:
84
√
6



Which statement explains the error Jordan made?



A.
Jordan multiplied first in Step 2 and should have added first. Since
4
√
3
+
5
√
6
=
9
√
9
, Step 1 is
9
√
9
(
8
√
2
)
.

B.
Jordan multiplied in Step 2 by multiplying the radicands and should have added the radicands. Since
5
√
6
(
8
√
2
)
=
40
√
8
, Step 1 is
4
√
3
+
40
√
8
.

C.
Jordan simplified the radical in Step 3 by not multiplying the coefficient by the perfect square factor. Since
40
√
12
=
160
√
3
, the Step 2 is
4
√
3
+
160
√
3
.

D.
Jordan added in Step 4 by adding the radicands. Since
4
√
3
+
80
√
3
=
(
4
+
80
)
√
3
, Step 4 is
84
√
3
.

Answer 1

D. Jordan made the error in Step 4 by adding the radicands. After Step 3 the expression is 4√3 + 80√3 = (4+80)√3 = 84√3, not 84√6.