Show that reciprocal of 3+2√2 is …
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Yogita Ingle 6 years ago
First of all, rationalise the denominator of the reciprocal of 3 + 2√2.
3+2√213+2√2×3−2√23−2√23−2√2(3)2−(2√2)23−2√29−83−2√2
After rationalising its denominator, we get ( 3 - 2√2 ) as a result.
Now, let us assume that ( 3 - 2√2 ) is an irrational number. So, taking a rational number i.e., 3 and subtracting from it.
We have ;
[ 3 - 2√2 - 3 ]
⇒ - 2√2
As a result, we get ( - 2√2 ) which is an irrational number.
Hence, the reciprocal of ( 3 + 2√2) is an irrational number.
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