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Find the Square Root the Following by Prime Factorization. 190969

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Question

Find the square root  the following by prime factorization. 

 190969

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Solution

Resolving 190969 into prime factors:
190969 = 19 x 19 x 23 x 23 

Grouping the factors into pairs of equal factors:
190969 = (19 x 19) x (23 x 23)
Taking one factor for each pair, we get the square root of 190969:
19 x 23 = 437

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Chapter 3: Squares and Square Roots - Exercise 3.4 [Page 38]

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RD Sharma Mathematics [English] Class 8
Chapter 3 Squares and Square Roots
Exercise 3.4 | Q 2.12 | Page 38

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