Definition Q: What number when squared equals 36? A: 6 Q: Is it the only answer? A: No 6 is called a square root of 36 -6 is also a square root of 36 Def: b is called a square root of the number a if b 2 =a.
Examples A square root of 36 is 6 Another square root of 36 is -6 A square root of 121 is 11 Another square root of 121 is -11 A square root of 0 is 0 A square root of -4 is Remarks: 1)Each positive number has two square roots: a positive square root and a negative square root 2)0 has a unique square root 3)Each negative number has no square root. NONE
Notation The positive square root of a number a is denoted by the radical symbol: It’s also called the principal square root of a. Examples:
Definition Def: b is called an n th root of the number a if b n =a. The principal n th root of a is denoted by index of the radical radical symbol radicand Q: What number when cubed equals 8? A: 2 Q: What number when raised to the fifth power equals -32? A: -2 because