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High School Mathematics
2.25 Important Points in Extraction of Square Roots of Real Numbers

1. The product obtained by multiplying a number by itself is called the square of the number.

2. If a number is expressed as the product of two equal factors one such factor is called the square root of the given number.

3. If a number can be written as the product of two equal factors, then the number is said to be a perfect square.

4. The positive equal factors of a number is called the principal square root of that number.

5. Square roots for number which are perfect squares can be found by factorization method.

6. If a number has n digits, its square has 2n-1 or 2n digits.

7. The square of the number ends with any one of the digits 0, 1, 4, 5, 6, and 9. The converse is not true.

8. Number ending with any one of the digits 2, 4, 7, and 8 are not perfect square numbers.

9. Laws:

i) a + b (a+b).

ii) a - b (a-b).

iii) a * b = (ab).

iv) (a/b) = a/b.

v) (x2 + y2) x2 + y2 or x+y.

vi) (x2 - y2) x2 - y2 or x-y.

Directions: Write the above properties on a sheet of paper and also write at least five examples for each property.

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