classify the following number as rational or irrational numbers 1) root 45 2) 3root 27 3) root 197
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(i) √45 = √( 3 × 3 × 5 )
√45 = 3√5
Now as we know that rational × irrational = irrational
so, √45 is irrational.
(ii) 3√27 = 3 × √( 3 × 3 × 3 )
3√27 = 3 × 3√3 = 9√3
Similarly, 9√3 is also irrational
(iii) √197 = ( please refer to attatchment )
Hence, √197 = 14.03..... Which is neither terminating nor repeating
So, √197 is also irrational.
cσncєpt = Here we have used on two concept
1. Rational × irrational = irrational
2. Irrational = Non terminating Non repeating.
Remember : Here you asled to classify whether following numbers were rational or irratinal. If someone ask to prove they are irrational then solution is different
нσρє ιт нєℓρѕ
нєяє ιѕ уσυя ѕσℓυтισи
(i) √45 = √( 3 × 3 × 5 )
√45 = 3√5
Now as we know that rational × irrational = irrational
so, √45 is irrational.
(ii) 3√27 = 3 × √( 3 × 3 × 3 )
3√27 = 3 × 3√3 = 9√3
Similarly, 9√3 is also irrational
(iii) √197 = ( please refer to attatchment )
Hence, √197 = 14.03..... Which is neither terminating nor repeating
So, √197 is also irrational.
cσncєpt = Here we have used on two concept
1. Rational × irrational = irrational
2. Irrational = Non terminating Non repeating.
Remember : Here you asled to classify whether following numbers were rational or irratinal. If someone ask to prove they are irrational then solution is different
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