# Square Root Of 23

*** Save when you purchase these worksheets as part of the Exponents and Square Roots Worksheet Bundle. . *** These practice problems cover estimating square roots. Questions include:* The square root of 23 is between which 2 integers? 4 and 5. It is closer to 5.Please check out the thumbnail images and the preview file above to see what the problems look like.

*7*

In 100 C.E., Nicomachus of Gerasa observed that 13 + 23 + 33 + … + n3 = (1 + 2 + 3 + … + n)2 Or “the sum of the cubes of 1 to n is the same as the square of their sum.” The diagram above demonstrates this neatly: Counting the individual squares shows that 1 × 12 + 2 × 22 + 3 × 32 + 4 × 42 + 5 × 52 + 6 × 62 = 13 + 23 + 33 + 43 + 53 + 63 = (1 + 2 + 3 + 4 + 5 + 6)2

*4*

*1*

YBC 7289 is a small clay disc containing a rough sketch of a square and its diagonals. Across one of the diagonals is scrawled 1,24,51,10 — a sexagesimal number that corresponds to the decimal number 1.4142129, an approximation of the square root of 2. Below is the answer to the problem of calculating the diagonal of a square whose sides are 0.5 units. This bears on the issue of whether the Babylonians had discovered Pythagoras’s theorem some 1,300 years before Pythagoras did.

*7*

*2*