The square root of 18769 consists of how many digits?

Correct option is D

Given:

Number = 18769

Solution:

To determine the number of digits in the square root of a number, we can group the digits of the number from right to left in pairs.

For the number 18769:Group the digits from right to left: 1 87 69

We have 3 groups: 1, 87, and 69.

The number of digits in the square root will be equal to the number of groups formed. In this case, there are 3 groups.

Therefore, the square root of 18769 consists of 3 digits.

Alternate Solution:

Consider the range of perfect squares:

10² = 100 (3 digits, square root has 2 digits)

100² = 10000 (5 digits, square root has 3 digits)

1000² = 1000000 (7 digits, square root has 4 digits)

If a perfect square has 'n' digits:

If 'n' is even, its square root has $$\frac n2$$​ digits.

If 'n' is odd, its square root has $$\frac {n+1}2$$​digits.

The number 18769 has 5 digits (an odd number).Number of digits in its square root = $$\frac{(5 + 1) } 2 = \frac 6 2$$​= 3 digits.