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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

☛ Check: NCERT Solutions for Class 8 Maths Chapter 6

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

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