Find the square roots of the following numbers by the Prime Factorisation Method.
(i) 729 (ii) 400 (iii) 1764 (iv) 4096 (v) 7744 (vi) 9604 (vii) 5929 (viii) 9216 (ix) 529 (x) 8100
Solution:
As we know, each prime factor in the prime factorization of the square of a number occurs twice the number of times than that of the prime factorization of the number itself. Let us use this to find the square root of a given square number by pairing the prime factors.
(i) 729 = 3 × 3 × 3 × 3 × 3 × 3
√729 = √(3 × 3 × 3 × 3 × 3 × 3)
= 3 × 3 × 3
= 27
(ii) 400 = 2 × 2 × 2 × 2 × 5 × 5
√400 = √(2 × 2 × 2 × 2 × 5 × 5)
= 2 × 2 × 5
= 20
(iii) 1764 = 2 × 2 × 3 × 3 × 7 × 7
√1764 = √(2 × 2 × 3 × 3 × 7 × 7)
= 2 × 3 × 7
= 42
(iv) 4096 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
√4096 = √(2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2)
= 2 × 2 × 2 × 2 × 2 × 2
= 64
(v) 7744 = 2 × 2 × 2 × 2 × 2 × 2 × 11 × 11
√7744 = √(2 × 2 × 2 × 2 × 2 × 2 × 11 × 11)
= 2 × 2 × 2 × 11
= 88
(vi) 9604 = 2 × 2 × 7 × 7 × 7 × 7
√9604 = √(2 × 2 × 7 × 7 × 7 × 7)
= 2 × 7 × 7
= 98
(vii) 5929 = 7 × 7 × 11 × 11
√5929 = √(7 × 7 × 11 × 11)
= 7 × 11
= 77
(viii) 9216 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3
√9216 = √(2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3)
= 2 × 2 × 2 × 2 × 2 × 3
= 96
(ix) 529 = 23 × 23
√529 = √(23 × 23)
= 23
(x) 8100 = 2 × 2 × 3 × 3 × 3 × 3 × 5 × 5
√8100 = √(2 × 2 × 3 × 3 × 3 × 3 × 5 × 5)
= 2 × 3 × 3 × 5
= 90
☛ Check: NCERT Solutions for Class 8 Maths Chapter 6
Video Solution:
Find the square roots of the following numbers by the Prime Factorisation Method. (i) 729 (ii) 400 (iii) 1764 (iv) 4096 (v) 7744 (vi) 9604 (vii) 5929 (viii) 9216 (ix) 529 (x) 8100
NCERT Solutions for Class 8 Maths Chapter 6 Exercise 6.3 Question 4
Summary:
The square roots of the following numbers by the prime factorisation method (i) 729 (ii) 400 (iii) 1764 (iv) 4096 (v) 7744 (vi) 9604 (vii) 5929 (viii) 9216 (ix) 529 (x) 8100 are (i) 27, (ii) 20, (ii) 42, (iv) 64, (v) 88, (vi) 98, (vii) 77, (viii) 96, (ix) 23 and (x) 90
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