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# Square Root Exercise 1.2.1 – Square Root – Class IX

The square root exercise 1.2.1 is related to the chapter – Square Root – Class IX – Karnataka State Syllabus mathematics Notes.

## Square Root Exercise 1.2.1

1. ### Find the square root of the following numbers by the factorization method

(i) 82944

Solution:

82944 = 210  x 34

= (25)2   x (32)2 √(82944) = √((25)2   x (32)) = 2x 32 = 288

(ii) 155236

Solution: 155236 = (2)2 x  (197)2

√(155236) = √((2)2   x (197)) = 2 x 197 = 394

(iii) 19881

Solution: 19881 = (3)2 x  (47)2

√(19881) = √((3)2   x (47)) = 2 x 47 = 141

### 2. Find the square root of the following numbers.

(i) 184.96

Solution:

= (184.96X100)100 = (18496)100 = ((2³)²x(17)²)10²

√(184.96) = √ ((2³)²x(17)²10²) = (2³)x(17)10
(136)10

= 13.6

(iii) 19.5364

Solution:

19.5364 = (19.5364×10000)10000
= (195364)10000 √(195364/10000) = √ ((2)²x(221)²⁄100²) = (2)x(221)⁄100
(442)100

= 4.42

### 3. Exploration:

Find the squares of the numbers 9, 10, 99, 100, 1000, and 9999.Tabulate these numbers. How many digits are there in the squares of a numbers when it has even number of digits and odd number of digits?

Solution:

9² = 81; digits-2
10² = 100; digits-3
99² = 9801; digits-4
100² = 10000; digits-5
990² = 998001; digits-6
1000² = 1000000; digits-7
9999² = 99980001; digits-8

2n if the number has even digits
2n-1 if the number has odd digits.

### 4. If a perfect square A has A digits, how many digits to you expect in √𝐀

Solution:
If a perfect square A has n digits then, √A has

(n)2 Digits if n is even
(n+1)2 Digits if n is odd.