Radicals and Rationals

Front

What is a radical in mathematics?

Back

A radical is an expression that includes a root, such as a square root or cube root. It is typically represented using the radical symbol (√).

Front

How do you convert a rational exponent to radical form?

Back

To convert a rational exponent to radical form, use the formula a^(m/n) = n√(a^m), where 'n' is the root and 'm' is the power.

Front

What is the product rule for radicals?

Back

The product rule states that √(a) * √(b) = √(a * b) for any non-negative numbers a and b.

Front

What is the quotient rule for radicals?

Back

The quotient rule states that √(a/b) = √(a) / √(b) for any non-negative numbers a and b, where b ≠ 0.

Front

How do you simplify the expression 4^(1/3) * 4^(4/3)?

Back

You can simplify it by adding the exponents: 4^(1/3 + 4/3) = 4^(5/3).

Front

What is the definition of a rational number?

Back

A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, where p is the numerator and q is the denominator (q ≠ 0).

Front

What is the difference between a rational number and an irrational number?

Back

A rational number can be expressed as a fraction of two integers, while an irrational number cannot be expressed as a simple fraction and has a non-repeating, non-terminating decimal expansion.

Front

How do you express a number in radical form?

Back

To express a number in radical form, you write it using a root symbol. For example, the number 8 can be expressed as 2√(2) or √(64).

Front

What is the simplified form of √(a^2)?

Back

The simplified form of √(a^2) is |a|, which represents the absolute value of 'a'.

Front

What is the process for rationalizing the denominator?

Back

To rationalize the denominator, multiply the numerator and denominator by a suitable radical that will eliminate the radical in the denominator.