x n

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n x

MTH 100

n x n x

Radical Expressions

n x

Square Roots (n = 2) • • • • The principal square root of a positive number x is a positive number y such that y

2

= x.

The square root of a negative number is not a real number (we will discuss imaginary numbers in more detail later).

For numeric expressions, the square root key on your scientific calculator can be very useful.

For variable expressions, absolute value bars are used to ensure that the expression remains positive (unless the problem states that all variables are positive).

Cube Roots (n = 3) • • • Cube roots are not subject to the same restrictions as square roots. Both the radicand and the result can be negative.

Some scientific calculators have a cube root key.

Absolute value bars are not necessary.

Other (larger) roots (n > 4) • • • Radicals with an even index are subject to the same rules as square roots.

Radicals with an odd index are subject to the same rules as cube roots.

Your scientific calculator has a key equipped to find larger roots.

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