8.1 Introduction to Square Roots Page 518

More Properties of Square Roots

* The square root of a perfect square number is a rational number. * the square root of a positive rational number that is not a perfect square is an irrational number. For example, (radical symbol)20 is an irrational number because 20 is not a perfect suare. * The square root of a negative real number is not a real number. For example, (radical symbol)-2 is not a real number.

Properties of Square Roots

*Every positive real number has two square roots, one positive and one negative. * The square root of 0 is 0. In symbols,( radical symbol) 0 = 0. *We use the symbol radical symbol called radical, to denote the non negative square root of a real number. The non negative square root is called the principal square root. *The number under the radical is called the radicand. For example, the radicand in (Radicand symbol) 25 is 25.

Negative real numbers do not have square roots that are real numbers

Example -16 Page 521

Square Root

For any real numbers a and b, b is a square root of a if b square = a.

Principal Square Root or non negative square root

The Non negative (zero or positive)

Radical

The Radical symbol

Radicand

The number under the radical symbol.