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Show that Each of the Following Numbers is a Perfect Square. Also, Find the Number Whose Square is the Given Number in Each Case: 14641 - Mathematics

Show that each of the following numbers is a perfect square. Also, find the number whose square is the given number in each case:

 14641 

 

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Solution

In  problem, factorise the number into its prime factor. 

14641 = 11 x 11 x 11 x 11
Grouping the factors into pairs of equal factors, we obtain:
14641 = (11 x 11) x (11 x 11)
No factors are left over. Hence, 14641 is a perfect square. The above expression is already grouped into equal factors:
14641 = (11 x 11) x (11 x 11)
            = (11 x 11)2
Hence, 14641 is the square of 121, which is equal to 11 x 11.

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APPEARS IN

RD Sharma Class 8 Maths
Chapter 3 Squares and Square Roots
Exercise 3.1 | Q 2.3 | Page 4
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