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Byju's Answer
Standard XII
Mathematics
Multinomial Expansion
What is the s...
Question
What is the square root of
2
plus the square root of
3
?
Open in App
Solution
√
2
+
√
3
is not readily simplifiable.
You can calculate an approximate value as:
√
2
+
√
3
≅
1.414213562
+
1.732050808
=
3.146264370
Funnily enough, I was intrigued the other day to find the simplest polynomial with integer coefficients of which
√
2
+
√
3
is a root.
The answer is :
x
4
−
10
x
2
+
1
=
0
which has roots:
√
2
+
√
3
√
2
−
√
3
−
√
2
+
√
3
−
√
2
−
√
3
and
x
4
−
10
x
2
+
1
has factors:
(
x
−
√
2
−
√
3
)
(
x
−
√
2
+
√
3
)
(
x
+
√
2
−
√
3
)
(
x
+
√
2
+
√
3
)
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