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Regents Exam Questions A2.N.2: Operations with Radicals
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A2.N.2: Operations with Radicals: Perform arithmetic operations (addition, subtraction,
multiplication, division) with expressions containing irrational numbers in radical form
1 The sum of
1)
6
2)
2a 2 b
3
3
6a 4 b 2 and
162a 4 b 2 , expressed in simplest radical form, is
168a 8 b 4
3
21a 2 b
20a 3 
2 Simplify:
3 Find the sum of
6ab 2
4a
4)
10a 2 b 3 8
45a 5
12a 3 and
45  ax
4 Simplify: 2ax
3
3)
27a 5 b 2 .
20
5 Simplify: 3 242x 5 y 5  11xy
2x 3 y 3
6 Express 5 3x 3  2 27x 3 in simplest radical form.
9x 5  18x 4 y 
7 Simplify:
Ê
8 If x  0, the expression ÁÁÁ
Ë
2x
1)
2)
4xy 6  8y 7
ˆÊ
x ˜˜˜ ÁÁÁ
¯Ë
2x
ˆ
2x ˜˜˜ is equivalent to
¯
3) x 2 2
4) x 2
ˆ˜ ÊÁ 3
ˆ˜
ÊÁ 3
9 The expression ÁÁÁÁ 27x 2 ˜˜˜˜ ÁÁÁÁ 16x 4 ˜˜˜˜ is equivalent to
¯Ë
¯
Ë
1)
2)
12x 2 3 2
12x 3 2x
3)
4)
10 What is the product of
1)
2)
3
4a 2 b 4 and
3
3
4ab 2 a 2
4a 2 b 3 3 a
16a 3 b 2 ?
3)
4)
11 Simplify:
3
xy
12 Simplify:
3
2a

xy
128x 6 y 2
81z 4
3
3
6x 2x 2
6x 2 3 2
3
8ab 2 a 2
8a 2 b 3 3 a
18a 3
(x  y) 5
16x 3 y 2
3z 7
1
ID: A
A2.N.2: Operations with Radicals: Perform arithmetic operations (addition, subtraction,
multiplication, division) with expressions containing irrational numbers in radical form
Answer Section
1 ANS: 3
3
6a 4 b 2  3 (27  6)a 4 b 2
a
3
6ab 2  3a
4a
3
3
6ab 2
6ab 2
REF: 011319a2
2 ANS:
(2a  3a 2 ) 5a
REF: 119313al
3 ANS:
(2a  3a 2 b)( 3a )
REF: 119209al
4 ANS:
8ax 5
REF: 089312al
5 ANS:
44x 2 y 2 2xy
REF: 019111al
6 ANS:
5 3x 3  2 27x 3  5 x 2
3x  2 9x 2
3x  5x
3x  6x
REF: 061032a2
7 ANS:
(3x 2  2y 3 ) x  2y
REF: 069709al
8 ANS: 4
9 ANS: 4
ˆÊ
ÊÁ 3
ÁÁ 27x 2 ˜˜˜ ÁÁÁ 3 16x 4
˜˜ ÁÁ
ÁÁ
¯Ë
Ë
REF: 010103a
ˆ˜
˜˜ 
˜˜
¯
3
3 3  2 4  x 6  3  2  x 2 3 2  6x 2 3 2
REF: 011421a2
1
3x  x
3x
ID: A
10 ANS: 1
3
64a 5 b 6 
3
4 3 a 3 a 2 b 6  4ab 2
3
a2
REF: 011516a2
11 ANS:
(x  y)
a
a
REF: 069709al
12 ANS:
2xz
3
REF: 019811al
2