#### Question

Find the number of digits in the square root of the following perfect squares

225

77841

1522756

47169424

Question

Find the number of digits in the square root of the following perfect squares

225

77841

1522756

47169424

The number of digits of the square root of a number is related to the number of digits of the number itself. If the number of digits of the number is even, the number of digits of its square root is half of the digit of the number. If the number of digits of the number is odd, the number of digits of its square root is the half of one plus the digit of the number.

225 - the number of digit n = 3

Therefore,

the number of digits of the square root of 225 is \dfrac{3+1}{2} = 2

77841 - the number of digit n = 5

Therefore,

the number of digits of the square root of 77841 is \dfrac{5+1}{2} = 3

1522756 - the number of digit n = 7

Therefore,

the number of digits of the square root of 1522756 is \dfrac{7+1}{2} = 4

47169424 - the number of digit n = 8

Therefore,

the number of digits of the square root of 1522756 is \dfrac{8}{2} = 4