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Byju's Answer
Standard IX
Mathematics
Multiplication of Surds
Simplify each...
Question
Simplify each of the following expressions:
(i)
(
3
+
√
3
)
(
2
+
√
2
)
(ii)
(
3
+
√
3
)
(
3
−
√
3
)
(iii)
(
√
5
+
√
2
)
2
(iv)
(
√
5
−
√
2
)
(
√
5
+
√
2
)
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Solution
We know that,
(
A
+
B
)
(
C
+
D
)
=
A
×
(
C
+
D
)
+
B
×
(
C
+
D
)
=
A
C
+
A
D
+
B
C
+
C
D
(i)
(
3
+
√
3
)
(
2
+
√
2
)
=
(
6
+
2
√
3
+
3
√
2
+
√
6
)
(ii)
(
√
5
+
√
2
)
2
=
(
5
+
2
+
2
√
10
)
=
(
7
+
2
√
10
)
(iii)
(
3
+
√
3
)
(
3
−
√
3
)
=
(
9
−
3
)
=
6
(iv)
(
√
5
−
√
2
)
(
√
5
+
√
2
)
=
(
5
−
2
)
=
3
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7
Similar questions
Q.
Simplify the following expressions:
(i)
(
5
+
√
7
)
(
2
+
√
5
)
(ii)
(
5
+
√
5
)
(
5
−
√
5
)
(iii)
(
√
3
+
√
7
)
(iv)
(
√
11
−
√
7
)
(
√
11
+
√
7
)
Q.
Simplify:
(i)
4
+
2
4
-
2
(ii)
5
+
3
5
-
3
(iii)
6
-
6
6
+
6
(iv)
5
-
2
2
-
3
(v)
5
-
3
2
(vi)
3
-
3
2
Q.
Simplify
(i)
3
-
11
3
+
11
(ii)
-
3
+
5
-
3
-
5
(iii)
3
-
3
2
(iv)
5
-
3
2
(v)
5
+
7
2
+
5
(vi)
5
-
2
2
-
3
Q.
Simplify each of the following:
(i) (x+3)
3
+ (x−3)
3
(ii)
x
2
+
y
3
3
-
x
2
-
y
3
3
(iii)
x
+
2
x
3
+
x
-
2
x
3
(iv) (2x − 5y)
3
− (2x + 5y)
3