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By considering square numbers, determine an approximation for root 83 to the nearest whole number.
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So in the question, it asked us to consider square numbers.
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So what are square numbers?
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Well, square numbers are the result of multiplying a number by itself.
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So, for example, one is a square number because one multiplied by one equals one.
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And four is a square number because two multiplied by two is equal to four.
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So then, if we list the next square numbers, we’ve got nine, 16, 25, 36, 49, 64, 81, and 100.
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And I stopped at 100 because that’s over the number that we’re looking at.
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And I say that because the number we’re looking at is 83 because what we want to consider is the square numbers either side of 83.
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So less than 83, we have 81, which is nine multiplied by nine.
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And then, greater than 83, we have 100, which is 10 multiplied by 10.
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Well, if we know that 83 is between 81 and 100, then therefore, root 83 must be between root 81 and root 100.
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And it must be greater than root 81 and less than root 100.
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And therefore, we can say that root 83 must be greater than nine.
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That’s because root 81 is equal to nine because nine multiplied by nine is 81.
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But it must be less than 10.
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And that’s because root 100 is equal to 10 because 10 multiplied by 10 is 100.
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Well, the question asks for an approximation for root 83 to the nearest whole number.
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So we need to decide whether it’s closer to nine or 10.
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Well, let’s think about 83 for a second.
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Well, 83 is only two greater than 81.
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However, it’s 17 less than 100.
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So therefore, 83 is closer to 81.
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So therefore, root 83 must be closer to root 81.
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So therefore, our approximation for root 83 to the nearest whole number is going to be nine.