Question

Find the square of the following numbers containing 5 in unit's place

Answer 1

(i) 15 (ii) 95 (iii) 105 (iv) 205

(i) (15)2 = 1 x (1 + 1) x 100 + 25

= 1 x 2 x 100 + 25

= 200 + 25 = 225

(ii) (95)2 = 9 x (9 + 1) x 100 + 25

= 9 x 10 x 100 + 25

= 9000 + 25 = 9025

(iii) (105)2 = 10 x (10 + 1) x 100 + 25

= 10 x 11 x 100 + 25

= 11000 + 25 = 11025

(iv) (205)2 = 20 x (20 + 1) x 100 + 25

= 20 x 21 x 100 + 25

= 42000 + 25 = 42025

Answer 2

Answer:

Concept:

Perfect squares are natural numbers that square another natural number.

An integer whose square root is not a whole number is referred to as a non-perfect square.

A number's square will conclude with the unit digit of the multiplication of a × a if the number's units place digit is a.

Step-by-step explanation:

Given:

Number 45

Find:

Find the square of the following number containing 5 in the unit's place

Solution:

      $45^{2}$ = n$5^{2}$

      It can be written as

      = n(n+1) hundred + $5^{2}$

      Substituting the values

       = 4×5 hundred +25

       By further calculation

        = 2000+25

        = 2025

The square of the number 45 containing 5 in the unit's place is 2025.

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