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Well, isn't that just a happy little question! The square root of 104 is between 10 and 11, closer to 10. So, the nearest integer to the square root of 104 is 10. It's like a little mathematical journey to find the perfect whole number to represent the square root of 104.
Deductive reasoning. Trial and error. You know that the square root of 112 will be roughly halfway between 10 and 11 because 112 is roughly halfway between 100 and 121. 10.5 x 10.5 = 110.25 10.58 x 10.58 = 111.9364 10.583 x 10.583 = 111.999889 which is close enough for me.
8√7. Since the square root of 4 is 2 you just keep dividing the number by 4 and multiplying 2 outside the radical until you get to a number not divisible by 4. (√448 = √[112*4] = 2√112) then (2√112 = 2√[28*4] = 4√28) then (4√28 = 2√[7*4] = 8√7)
The first 51 squares of natural numbers are: ... 112 = 121: 122 = 144: 132 = 169: 142 = 196: 152 = 225: 162 = 256: 172 = 289: 182 ... I am now going to list the square numbers with their roots, just to be helpful. ... by looking at the prime factors of 17640 that the square root of 17640 is not a whole number? YES Partially NO. and thank you
112 = 121122 = 144 is your answer