Converting Radical forms

Front

What is a radical expression?

Back

A radical expression is an expression that includes a root, such as a square root, cube root, etc. For example, √x or ∛(x+1).

Front

How do you convert a radical expression to an exponential form?

Back

To convert a radical expression to exponential form, use the formula: √a = a^(1/2) and ∛a = a^(1/3).

Front

What is the rational exponent for the square root of x?

Back

The rational exponent for the square root of x is x^(1/2).

Front

What is the rational exponent for the cube root of y?

Back

The rational exponent for the cube root of y is y^(1/3).

Front

Convert (xy)^(11/4) to radical form.

Back

(xy)^(11/4) = 4√(xy^11).

Front

What is the relationship between radical and rational exponents?

Back

Radical exponents can be expressed as rational exponents, where the index of the root becomes the denominator of the exponent.

Front

How do you express x^(3/2) in radical form?

Back

x^(3/2) = √(x^3) or (√x)^3.

Front

What is the exponential form of √(a^5)?

Back

The exponential form of √(a^5) is a^(5/2).

Front

Convert 4√(x^2) to exponential form.

Back

4√(x^2) = 4 * x^(2/4) = 4 * x^(1/2).

Front

What is the value of (x^4)^(1/2)?

Back

The value of (x^4)^(1/2) is x^(4*1/2) = x^2.