Question

b. 1936 soldiers are to be arranged in such a way that numbers columns is equal to the no of rows. Find the number of soldiers in a row.​

Answer 1

Answer:

For obtaining equal number of rows and equal number of soldiers in it, we've to take the square root of 1936

using L.C.M method/Division Method

√1936=44

as we know

44×44=44²=1936

therefore

the number of rows should be 44 and 44 soldiers should be there in each row.

hope it helps

Answer 2

$\green{\large\underline{\sf{Solution-}}}$

Given that,

• 1936 soldiers are to be arranged in such a way that number of columns is equal to the number of rows.

Let assume that

• Number of rows = x

So,

• Number of soldiers in each row = x

Thus,

• Total number of soldiers = x × x

According to statement, it is given that

Total number of soldiers = 1936

$\rm \implies\: {x}^{2} = 1936$

$\rm \implies\:x = \sqrt{1936}$

So, using prime factorization method, we have

$\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:1936 \:\:}}}\\ {\underline{\sf{2}}}& \underline{\sf{\:\:968 \:\:}} \\\underline{\sf{2}}&\underline{\sf{\:\:484\:\:}} \\ {\underline{\sf{2}}}& \underline{\sf{\:\:242 \:\:}} \\ {\underline{\sf{11}}}& \underline{\sf{\:\:121 \:\:}} \\ {\underline{\sf{11}}}& \underline{\sf{\:\:11 \:\:}} \\\underline{\sf{}}&{\sf{\:\:1 \:\:}} \end{array}\end{gathered}$

$\rm \implies\:x = \sqrt{2 \times 2 \times 2 \times 2 \times 11 \times 11}$

$\rm \implies\:x = 2 \times 2 \times 11$

$\bf\implies \:x = 44$

So, it means

Number of soldiers in each row = 44

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Additional Information :-

1. Between two consecutive natural numbers, n and n + 1, 2n natural numbers lies in between them.

2. Perfect square natural numbers can never ends with the digit 2, 3, 7, 8 and odd number of zeroes.

3. If a natural number consists of 2n number of digits, then square root of this number has 'n' digits.

4. If a natural number consists of 2n + 1 number of digits, then square root of this number has 'n' digits.