1.2 Learn Basic Properties and Operations

Radicals

A radical , also called a root, is the opposite of an exponent. Finding a square root is the opposite of squaring a number. The bracket symbol $$\sqrt {\;} $$ indicates a square root.

Examples

$${8^2} = 64$$	8 squared is 64.
$$\sqrt {64} = 8$$	The square root of 64 is 8.

You may have noticed that –8 could also be the square root of 64 because $$( - 8)( - 8) = 64$$. Most real-life situations require the positive root, but in special situations both roots may be needed. We can show both roots in this way: $$\sqrt {16} = \pm 4$$, which means “the square root of 16 is plus or minus 4.”

A cube root is the opposite of raising a number to the third power. An index number is written in the angle of the bracket to show which root is meant.

Examples

	$$\sqrt[3]{8} = 2$$	The cube root of 8 is 2 because $${2^3} = 8$$.
	$$\sqrt[4]{{625}} = 5$$	The fourth root of 625 is 5 because $${5^4} = 625$$.

A cube root can be negative: $$\sqrt { - 27} = - 3$$ because $$( - 3)( - 3)( - 3) = - 27$$.