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if I wanted to estimate 59−−√, the first step would be to find the two ______ squares that 59 lies _______ on the number line. The closest perfect square less than 59 is ______. The closest perfect square greater than 59 is _______. I could then think about the number 59 and how close it is to the smaller perfect square and the larger perfect square. I could then take the _________ root of the perfect squares to see how I would estimate 59−−√. The 59−−√ is closest to _________

eh? surely, 59 is closer to 64 than it is to 49.

So √59 is closer to 8 than it is to 7.

Apologies for the confusion. You are correct. The closest perfect square less than 59 is 49, and the closest perfect square greater than 59 is 64. Since 59 is closer to 64 than it is to 49, the square root of 59 (√59) is closer to 8 than it is to 7.

If I wanted to estimate 59−−√, the first step would be to find the two perfect squares that 59 lies between on the number line. The closest perfect square less than 59 is 49. The closest perfect square greater than 59 is 64. I could then think about the number 59 and how close it is to the smaller perfect square and the larger perfect square. I could then take the square root of the perfect squares to see how I would estimate 59−−√. The 59−−√ is closest to 7.