Radicals and Rational Exponents

Front

What is a radical?

Back

A radical is an expression that includes a root, such as a square root (√) or cube root (∛).

Front

What is a rational exponent?

Back

A rational exponent is an exponent that is a fraction, representing both a power and a root. For example, x^(1/2) is the square root of x.

Front

Convert the radical expression √x to exponential form.

Back

x^(1/2)

Front

Convert the expression x^(3/4) to radical form.

Back

The radical form is the fourth root of x cubed: ∛(x^3).

Front

What is the principal square root of a number?

Back

The principal square root of a number is the non-negative root. For example, the principal square root of 9 is 3.

Front

How do you simplify √(-1)?

Back

√(-1) simplifies to i, where i is the imaginary unit.

Front

What is the value of √(-4)?

Back

The value of √(-4) is 2i.

Front

Simplify the expression (√(x^2)).

Back

The simplified expression is |x|, the absolute value of x.

Front

What is the relationship between radicals and rational exponents?

Back

Radicals can be expressed as rational exponents; for example, √x = x^(1/2).

Front

How do you simplify the expression 5√(x^2)?

Back

The simplified expression is 5|x|.