Roots We call a radicand and b root.

Examples: the square root of one hundred is ten

NOTE: You must memorize the first squares:
12=1        22=4       32=9       42=16     52=25
62=36      72=49      82=64     92=81     102=100
112=121  122=144   132=169  142=196  152=225
202=400  252=625   302=900
(n+1)2= n2+ n + (n + 1)

The numbers which have an exact square root are called perfect squares. If the number isn't a perfect square, we find the whole square root, which is the highest perfect square that is lower than the number.

Example:
√108≈10    and the remainder is 8
√200≈14    and the remainder is 4

A whole number can have:

-two square roots (which are whole numbers):
√9 = 3  because 32 = 9
√9 = -3 because (-3)2 = 9

We usually name these two square roots with  √9   and   -√9

-two square roots (which aren’t whole numbers):
√2 = 1.4142...

-one square root:
√0 = 0

-no square roots:
√(-4)

Exercise: Calculate:
a) √123
b) √207
c) √-9
d) -√121

Solutions: a) 11 and remainder 2; b) 14 and remainder 11; c) it doesn't exist; d) -11