simplify (square root 3 - square root 2)
Answers
Answered by
2
Answer:
(
3
+
2
)
2
=5+2
6
Step-by-step explanation:
Given : Expression (\sqrt{3} +\sqrt{2})^2(
3
+
2
)
2
To find : Simplify the expression ?
Solution :
Using algebraic identity,
(a+b)^2=a^2+b^2+2ab(a+b)
2
=a
2
+b
2
+2ab
Here, a=\sqrt{3},\ b=\sqrt{2}a=
3
, b=
2
(\sqrt{3} +\sqrt{2})^2=(\sqrt{3})^2+(\sqrt{2})^2+2(\sqrt{3})(\sqrt{2})(
3
+
2
)
2
=(
3
)
2
+(
2
)
2
+2(
3
)(
2
)
(\sqrt{3} +\sqrt{2})^2=3+2+2\sqrt{6}(
3
+
2
)
2
=3+2+2
6
(\sqrt{3} +\sqrt{2})^2=5+2\sqrt{6}(
3
+
2
)
2
=5+2
6
Therefore, (\sqrt{3} +\sqrt{2})^2=5+2\sqrt{6}(
3
+
2
)
2
=5+2
6
Answered by
1
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