Answer :
Answer:
zfv c
fggcdv
Step-by-step explanation:
db fvcvvcçßfvxfvvvvvvbb
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
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
(ii) 400 = 2 × 2 × 2 × 2 × 5 × 5
√400 = √(2 × 2 × 2 × 2 × 5 × 5)
= 2 × 2 × 5
= 20
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
(iii) 1764 = 2 × 2 × 3 × 3 × 7 × 7
√1764 = √(2 × 2 × 3 × 3 × 7 × 7)
= 2 × 3 × 7
= 42
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
(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
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
(v) 7744 = 2 × 2 × 2 × 2 × 2 × 2 × 11 × 11
√7744 = √(2 × 2 × 2 × 2 × 2 × 2 × 11 × 11)
= 2 × 2 × 2 × 11
= 88
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
(vi) 9604 = 2 × 2 × 7 × 7 × 7 × 7
√9604 = √(2 × 2 × 7 × 7 × 7 × 7)
= 2 × 7 × 7
= 98
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
(vii) 5929 = 7 × 7 × 11 × 11
√5929 = √(7 × 7 × 11 × 11)
= 7 × 11
= 77
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
(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
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
(ix) 529 = 23 × 23
√529 = √(23 × 23)
= 23
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
(x) 8100 = 2 × 2 × 3 × 3 × 3 × 3 × 5 × 5
√8100 = √(2 × 2 × 3 × 3 × 3 × 3 × 5 × 5)
= 2 × 3 × 3 × 5
= 90
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
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
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
(ii) 400 = 2 × 2 × 2 × 2 × 5 × 5
√400 = √(2 × 2 × 2 × 2 × 5 × 5)
= 2 × 2 × 5
= 20
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
(iii) 1764 = 2 × 2 × 3 × 3 × 7 × 7
√1764 = √(2 × 2 × 3 × 3 × 7 × 7)
= 2 × 3 × 7
= 42
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
(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
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
(v) 7744 = 2 × 2 × 2 × 2 × 2 × 2 × 11 × 11
√7744 = √(2 × 2 × 2 × 2 × 2 × 2 × 11 × 11)
= 2 × 2 × 2 × 11
= 88
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
(vi) 9604 = 2 × 2 × 7 × 7 × 7 × 7
√9604 = √(2 × 2 × 7 × 7 × 7 × 7)
= 2 × 7 × 7
= 98
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
(vii) 5929 = 7 × 7 × 11 × 11
√5929 = √(7 × 7 × 11 × 11)
= 7 × 11
= 77
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
(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
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
(ix) 529 = 23 × 23
√529 = √(23 × 23)
= 23
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
(x) 8100 = 2 × 2 × 3 × 3 × 3 × 3 × 5 × 5
√8100 = √(2 × 2 × 3 × 3 × 3 × 3 × 5 × 5)
= 2 × 3 × 3 × 5
= 90
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