Classify the following numbers as rational or irrational : (i) square root of 23 (ii) square root of 225 (iii) 0.3796 (iv) 7.478478 ... (v) 1.101001000100001 ...
Question
Classify the following numbers as rational or irrational :
(i) $\sqrt{23}$
(ii) $\sqrt{225}$
(iii) 0.3796
(iv) $7.478478 \ldots$
(v) $1.101001000100001 \ldots$
Answer
Let's classify these numbers based on their properties and the general definitions of rational and irrational numbers:
- $\sqrt{23}$: This number is irrational. Square roots of non-perfect squares are always irrational.
- $\sqrt{225}$: This is equal to 15, which is a rational number since it can be expressed as $\frac{15}{1}$.
- 0.3796: This is rational because it is a terminating decimal, which can be expressed as a fraction.
- $7.478478\ldots$: This number is rational because it has a repeating pattern, which means it can be expressed as a fraction.
- $1.101001000100001\ldots$: This number is irrational. It presents a non-repeating, non-terminating pattern that cannot be expressed as a fraction.
Remember, rational numbers are any numbers that can be represented as the quotient of two integers, $\frac{p}{q}$, where $q \neq 0$. Irrational numbers cannot be so expressed.
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