# Find the number of digits in the square root of each of the following numbers (without any calculation).

(i) 64 (ii) 144 (iii) 4489 (iv) 27225 (v) 390625

**Solution:**

If a perfect square is of n digits then its square root will have n/2 digits if n is even and (n + 1)/2 if n is odd

(i) 64

n = 2 (even)

Number of digits in its square root = 2/2 = 1

(ii) 144

n = 3 (odd)

Number of digits in its square root = (n + 1)/2 = (3 + 1)/2 = 4/2 = 2

(iii) 4489

n = 4 (even)

Number of digits in its square root = n/2 = 4/2 = 2

(iv) 27225

n = 5 (odd)

Number of digits in its square root = (n + 1)/2 = (5 + 1)/2 = 6/2 = 3

(v) 390625

n = 6 (even)

Number of digits in its square root = n/2 = 6/2 = 3

**Video Solution:**

## Find the number of digits in the square root of each of the following numbers (without any calculation). (i) 64 (ii) 144 (iii) 4489 (iv) 27225 (v) 390625

### NCERT Solutions for Class 8 Maths - Chapter 6 Exercise 6.4 Question 2

**Summary:**

The number of digits in the square root in the given perfect squares (i) 64 (ii) 144 (iii) 4489 (iv) 27225 (v) 390625 are (i) 1, (ii) 2, (iii) 2, (iv) 3, (v) 3