Square Root EXERCISE 1.1.1
- 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)2 ) = 25 x 32 = 288
(ii) 155236
Solution:
155236 = (2)2 x (197)2
√(155236) = √((2)2 x (197)2 ) = 2 x 197 = 394
(iii) 19881
Solution:
19881 = (3)2 x (47)2
√(19881) = √((3)2 x (47)2 ) = 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)²⁄10²) = (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
They follow the rule
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.
