Question

find the number of digits in spuare root of 10201. a)2 b)3 c)4 d)5. with explain.
Q.2 sum of first n odd natural number a)n(n+1) b) n(n-1) c) n^2 d) (n+1)^2​

Answer 1

To find,

(a) The number of digits in the square root of 10201.

(b) Sum of first n odd natural number

Solution,

We can solve this mathematical question by the following method.

(a) The square root of 10201 is 101.

Thus, the number of digits in the square root of 10201 is 3. (Option B)

We can re-verify the square root of 10201 by multiplying 101 two times.

Thus, we can say that the square root of 10210 is 101 and the number of digits in 101 is 3.

As a result, option B is correct.

(b) The sum of the first n odd natural number is n². (Option C)

Here, we need to find the sum of first n odd natural numbers.

∴ Sum of 1,3,5,7,9 to infinity

First-term = 1 = a

Common difference = 2 = d

∴ Sum of n natural odd numbers = $\frac{n}{2}(2a+(n-1)d)$

                                                       = $\frac{n}{ 2} (2+(n-1)2)$

                                                       = $\frac{n}{2} (2n)$

                                                       = n²

As a result, the sum of first n natural odd numbers is n². (Option c)