How do you simplify $$\frac{a^m}{a^n}$$ ?

You simplify it by subtracting the exponents: $$a^{m-n}$$ .

What is the cube root of $$56r^8s^4$$ ?

The cube root simplifies to $$2r^2s \\cdot \\sqrt[3]{7r^2s}$$ .

How do you express $$\sqrt{a^2}$$ ?

$$\sqrt{a^2} = |a|$$ , which means the absolute value of a.

What is a perfect square?

A perfect square is a number that can be expressed as the square of an integer, such as 1, 4, 9, 16, etc.

What is the nth root of a number?

The nth root of a number x is a number r such that $$r^n = x$$ .

What is the difference between a square root and a cube root?

A square root is a number that, when multiplied by itself, gives the original number, while a cube root is a number that, when multiplied by itself three times, gives the original number.

What does it mean for a radical to be in simplest form?

A radical is in simplest form when there are no perfect squares (or cubes) under the radical sign and no fractions under the radical.

How do you combine radicals?

You can combine radicals by adding or subtracting them if they have the same index and radicand, e.g., $$\sqrt{2} + \sqrt{2} = 2\sqrt{2}$$ .

Simplifying Radicals and nth Roots Flashcards

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1.

FLASHCARD QUESTION

Front

What is a radical?

Back

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

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