Page 28 - ArithBook5thEd ~ BCC

8. Evaluate 10 3

9. Complete the following table of squares:
2
2
2
2
0 =0 6 = 12 = 18 =
2
2
2
2
1 = 7 =49 13 = 19 =
2
2
2
2
2 = 8 = 14 = 20 =
2
2
2
2
3 = 9 = 15 = 30 =
2
2
2
2
4 = 10 = 16 = 40 =
2
2
2
2
5 = 11 = 17 = 50 =
10. Complete the following table of cubes:
3
3
3
3
0 = 3 = 6 = 9 =
3
3
3
3
1 = 4 =64 7 = 10 =
3
3
3
3
2 = 5 = 8 = 100 =
1.4.3 Square Roots
If there is a number, whose square is the number n, we call it the square root of n,and symbolize it by
√
n.
2
For example, 2 = 4, so 2 is the square root of 4, and we write
√
4= 2.
2
Similarly, 3 = 9, so 3 is the square root of 9, and we write
√
9= 3.
Actually, every positive whole number has two square roots, one positive and one negative. The positive
square root is called the principal square root, and, for now, when we say square root, we mean the
principal one.
A whole number whose square root is also a whole number is called a perfect square. The first few
perfect squares are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121. Clearly, there are lots of whole numbers
that are not perfect squares. But these numbers must have square roots. Using our geometric intuition,
it is easy to believe that there are geometric squares whose areas are not perfect square numbers. For
example, if we want to construct a square whose area is 5 square units, we could start with a square
whose area is 4 square units, and steadily expand it on all sides until we get the desired square.
3
√
2 5

Area=4 Area = 5 Area = 9

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