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Powers and roots: square roots. |
| First two years of secondary education. | |
| Perfect square roots. | |
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We know that 25 is a perfect square. It is the square of 5. The same thing occurs with 49. It is the square of 7. Therefore, we can say that 5 is the square root of 25 and 7 is the square root of 49. The sign used to denote square root is Therefore, we can say Ö25 = 5 as 52 = 25. The number from which a root is to be found is called a radicand. In the previous example the radicand was 25. Working out the square root of a number is the reverse operation of working out the square of a number. Geometrically speaking, finding the square root of a number is the same as finding the length of the side of a square whose area is equal to the number given. | |
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14. Use the table of square numbers as a point of reference to find the square roots of the following numbers: 4, 9, 36, 81, 100, 121, 225 | |
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Check your answers in the following window. | |
| Inexact square roots. | |
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60 is not a perfect square. Therefore, its square root is not an exact number
and is not a natural number. 60 lies between the perfect squares 49 and 64.
49 < 60 < 64
Therefore, the square root lies somewhere between 7 (the square root of 49)
and 8 (the square root of 64). So, we can say that 7 is the nearest whole square root of
60. The difference is 60 - 72 = 60 - 49 = 11 which is
referred to as the remainder of the square root. 60 = 72 + 11 In other words, this number is equal to the square of the
nearest whole square root plus the remainder.
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14. Work out the nearest whole square root and the remainder of the following
numbers:
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Check your results in the following window. | |
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| Fernando Arias Fernández-Pérez | ||
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| Spanish Ministry of Education. Year 2001 | ||
Except where otherwise noted, this work is licensed under a Creative Common License
