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Question

Write the prime factorization of the following numbers and hence find their square roots.
(i) 7744 (ii) 9604
(iii) 5929 (iv) 7056

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Solution

Factorization, we get :
(i) 7744 = 2×2×2×2×2×2×11×11

Square root of 7744
=7744=2×2×2×2×2×2×11×11
Grouping the factors in pairs of equal factors,
7744=2×2×2×2×7×7
Square root of 7744 = 88

(ii) 9604=2×2×2×2×7×7

Square root of 9604
9604=2×2×7×7×7×7
= 2×7×=98

(iii) 5929=7×7×11×11

Square root of 5929
=5929=7×7×11×11
= 7×11=77

(iv) 7056=2×2×2×2×3×3×7×7

Square root of 7056
= 7056=2×2×2×2×3×3×7×7
= 2×2×3×7=84


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