The square root of a perfect square of n digits will have n/2 digits if n is even. State whether the statement is true or false.

Solution:

Given, the square root of a perfect square of n digits will have n/2 digits if n is even.

We have to determine if the given statement is true or false.

Example: consider a perfect square 64

Number of digits, n = 2

n is even.

Square root of 64 = √64 = 8

n/2 = 2/2 = 1

Number of digits in square root = 1

Therefore, if a perfect square is of n digits, then its square root will have n/2 digit if n is even.

✦ Try This: The square root of a perfect square of n digits will have (n+1)/2 digits if n is odd. State whether the statement is true or false.

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 3 Sample Problem 19

The square root of a perfect square of n digits will have n/2 digits if n is even. State whether the statement is true or false

Summary:

The given statement, ”The square root of a perfect square of n digits will have n/2 digits if n is even” is true

☛ Related Questions:

• Express 36 as a sum of successive odd natural numbers
• Check whether 90 is a perfect square or not by using prime factorisation
• Check whether 1728 is a perfect cube by using prime factorisation