Notes on Squares and Square Roots

1² = 1 ·1 = 1,     2² = 2 ·2 = 4,    3² = 3 ·3 = 9,     4² = 4 ·4 = 16,    5² = 5 ·5 = 25,
    6² = 6 ·6 = 36,     7² = 7 ·7 = 49,     8² = 8 ·8 = 64,    9² = 9 ·9 = 81,     10² = 10 ·10 = 100,    �

These are the square numbers. The square root is denoted by the symbol �{      }. The square root is either a positive or a negative number. For instance �4 = 2 and �4 = -2.

Examples:

(1) �[27] = 9 ·3 = 3 �3

(2) �[64] = 2·2 ·2 ·2 ·2 ·2 = 2 ·2 ·2 = 8

(3) �[72] = 2 ·2 ·2 ·3 ·3 = 2 ·3�2 = 6�2

(4) �[56] = 2 ·2 ·2 ·7 = 2 ·�{2 ·7} = 2 �[14]

Simplify the following square roots.

(1) �[25]

(2) �[75]

(3) �[125]

(4) �[48]

(5) �[324]

(6) �[576]

(7) �8

(8) �[196]

(9) �[441]

(10) �[225]