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CBSE Class 9 Answered

<div>Show that&nbsp;<img class="Wirisformula" src="https://images.topperlearning.com/topper/tinymce/integration/showimage.php?formula=e6d11f972eb8fb291df0894a6727155e.png" alt="square root of blank end root" align="middle" />7 - &nbsp;3 is irrational</div>
Asked by gpnkumar0 | 05 Sep, 2016, 08:55: PM
Expert Answer
begin mathsize 12px style To space prove colon space square root of 7 minus 3 space is space irrational
Suppose space square root of 7 minus 3 space is space rational rightwards double arrow square root of 7 minus 3 equals straight p over straight q space where space straight p comma space straight q space are space integers space and space straight q not equal to 0
So comma space square root of 7 minus 3 equals straight p over straight q rightwards double arrow square root of 7 equals straight p over straight q plus 3 equals fraction numerator straight p plus 3 over denominator straight q end fraction
But space we space know space that space square root of 7 space is space irrational comma space so space has space to space be space fraction numerator straight p plus 3 over denominator straight q end fraction space irrational.
But space since space straight p space and space straight q space are space integers comma space fraction numerator straight p plus 3 over denominator straight q end fraction space is space rational.
This space is space straight a space contradiction. space So comma space our space assumption space that space square root of 7 minus 3 space is space rational space is space false.
Hence comma space square root of 7 minus 3 space is space irrational. end style
Answered by Rebecca Fernandes | 05 Sep, 2016, 10:22: PM
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