A2-5.1 FLASHCARD Root and Rational Exponents

Front

What is a root in mathematics?

Back

A root of a number is a value that, when raised to a certain power (the degree of the root), gives the original number. For example, the square root of 9 is 3 because 3^2 = 9.

Front

Define nth root.

Back

The nth root of a number 'a' is a number 'b' such that b^n = a. It is denoted as @@ oot{n}{a}@@.

Front

What is the cube root of 8?

Back

Front

What is the fourth root of 256?

Back

Front

What is the fifth root of -243?

Back

Front

Explain the concept of real roots.

Back

Real roots are the solutions to equations that can be represented on the number line. They can be positive, negative, or zero.

Front

What does it mean if an equation has no real roots?

Back

An equation has no real roots if there are no real numbers that satisfy the equation, often occurring when taking an even root of a negative number.

Front

What is the square root of -16?

Back

The square root of -16 has no real solutions, as there is no real number that, when squared, gives a negative result.

Front

How do you simplify @@ oot{5}{-32}@@?

Back

@@ oot{5}{-32}@@ simplifies to -2, since -2 raised to the power of 5 equals -32.

Front

What is the difference between even and odd roots?

Back

Even roots (like square roots) can only yield real results for non-negative numbers, while odd roots (like cube roots) can yield real results for both positive and negative numbers.