Question
If n is a natural number, then $\sqrt{\text{n}}$ is:
✓
Answer
- sometimes a natural number and sometimes an irrational number.
Solution:
- Is incorrect, because $\sqrt{\text{n}}$ can not be always a natural number
i.e. if $\text{n}=2, \ \sqrt{\text{n}}=\sqrt{2}$ (not a natural no.)
- Is incorrect, similiarly, if n = 2, 5, …. Or any odd no. or not perfect square, $\sqrt{\text{n}}=\sqrt{2},\sqrt{5},\sqrt{7}$ are Non-terminating and non-repeating, So irrational in nature, So, not always a rational number.
- Is also incorrect, $\sqrt{\text{n}}$ can aslo be rational or say a natural number. If n = 4, 9, 16... or any perfect square number then $\sqrt{\text{n}}=2,3,4...$ natural numbers.
- Is fully correct because if n is any odd number or non-perfect square number then $\sqrt{\text{n}}$ would be irrational, but if n is a perfect square number $\sqrt{\text{n}}$ then will be a natural number.
If n = 2, 3, 5, 8 ... $\sqrt{\text{n}}=\sqrt{2},\sqrt{3},\sqrt{8}...$ (irrational)
If n = 4, 9, 16 ... = 2, 3, 4 ... (Natural number)
So, correct option is (d).
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A solid ball od radius $6\ cm$ is melted and then drawn into a wire of diameter $0.2\ cm.$ The length of wire is:
→Write the correct answer in the following: Degree of the zero polynomial is.
If $\bar{\text{x}}$ is the mean of $x_1, x_2, ..., x_n$ then for $\text{a}\neq0,$ the mean $ax_1, ax_2, ..., ax_n, \frac{\text{x}_1}{\text{a}},\frac{\text{x}_2}{\text{a}},\ \dots,\frac{\text{x}_\text{n}}{\text{a}}$ is:
→The mid-points of the sides of a triangle ABC along with any of the vertices as the fourth point make a parallelogram of area equal to:
→- $\text{ar}(\triangle\text{ABC})$
- $\frac{1}{2}\text{ar}(\triangle\text{ABC})$
- $\frac{1}{3}\text{ar}(\triangle\text{ABC})$
- $\frac{1}{4}\text{ar}(\triangle\text{ABC})$
The number $1.\overline{27}$ in the form $\frac{\text{p}}{\text{q}},$ where p and q are integers and $\text{q}\neq0,$ is:
→If $x^{140} + 2x^{151} + k$ is divisible by $x + 1,$ then the value of $k$ is:
→Write the correct answer in the following:
Mode of the data 15, 14, 19, 20, 14, 15, 16, 14, 15, 18, 14, 19, 15, 17, 15 is:
Mode of the data 15, 14, 19, 20, 14, 15, 16, 14, 15, 18, 14, 19, 15, 17, 15 is:
The factors of $a^2 - 1 - 2x - x^2$ are:
→Write the correct answer in the following:
The decimal expansion of the number $\sqrt{2}$ is.
→The decimal expansion of the number $\sqrt{2}$ is.