 # RD Sharma Solutions Class 8 Mathematics Solutions for Squares and Square Roots Exercise 3.5 in Chapter 3 - Squares and Square Roots

A General arranges his soldiers in rows to form a perfect square. He finds that in doing so, 60 soldiers are left out. If the total number of soldiers be 8160, find the number of soldiers in each row

We know that the total number of soldiers = 8160

Number of soldiers left out = 60

Number of soldiers arranged in rows to form a perfect square = 8160 – 60 = 8100

∴ number of soldiers in each row = √8100

= √ (9×9×10×10)

= 9×10

= 90

Video transcript
[Music] hello dear students i am sunita nair from leader learning i am here to help you solve the sum which goes like this a general arranges his soldiers in rows to form a perfect he finds that in doing so 60 soldiers are left out if the total number of soldiers be [Music] 8160 find the number of soldiers in each row all right so let's start working out the sum so the number of total number of soldiers is eight thousand one hundred and sixty all right now out of these he found that in forming in trying to form a perfect square sixty soldiers were left out so let us also leave out those 60 soldiers right so if we remove those 60 soldiers we will be left with 8100 so it apparently these 8100 soldiers fit into the square pattern this perfect square pattern quite nicely so he wants to know we want to know find the number of soldiers in each row so if we want to know the number of soldiers in each row we are basically finding out the side of the square right so the side of the square is nothing but the square root of 8100 so let's find the square root of 8100 we can do it by factorization method [Music] let's start with two again two three again three [Music] three again [Music] once more five and five right so the square root of eight thousand one hundred will be so let's take one from each of these space [Music] so that will be two multiplied by three multiplied by three multiplied by five so that gives us ninety [Music] so this is our answer so the number of soldiers in each row is ninety [Music] i hope you understood the explanation please drop a comment in the comment section you can visit our channel regularly for more homework solutions do subscribe if you find it useful thank you [Music]
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