√2+√3+√7 find the simplest rationalising factor
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Answer:
Step-by-step explanation:
(2+
3
+
5
)(2+
3
−
5
)=(2+
3
)
2
−(
5
)
2
=4+3+4
3
−5=7+4
3
−5
=2+4
3
=2(1+2
3
)
Now, conjugate of factor 1+2
3
is 1−2
3
=(1+2
3
)(1−2
3
)=1
2
−(2
3
)
2
=1−4×3=−11
∴(2+
3
+
5
)(2+
3
−
5
)(1−2
3
)
=2(1+2
3
)(1−2
3
)
=2(1
2
−(2
3
)
2
)=2(1−12)=−22,which is rational
Hence, (2+
3
−
5
)(1−2
3
) is the simplest rationalising factor of 2+
3
+
5
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