Simplifying Radicals with Variables

Front

What is a radical in mathematics?

Back

A radical is a symbol used to represent the root of a number, most commonly the square root. For example, √4 represents the square root of 4.

Front

What does it mean to simplify a radical?

Back

To simplify a radical means to express it in its simplest form, removing any perfect square factors from under the radical sign.

Front

How do you simplify √(a^2)?

Back

√(a^2) simplifies to |a|, which is the absolute value of a.

Front

What is the square root of 36?

Back

The square root of 36 is 6.

Front

How do you simplify √(12)?

Back

√(12) can be simplified to 2√3, since 12 = 4 * 3 and √4 = 2.

Front

What is the product property of square roots?

Back

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

Front

How do you simplify √(x^2y)?

Back

√(x^2y) simplifies to x√y, assuming x is non-negative.

Front

What is the sum of √(2) + √(8)?

Back

√(2) + √(8) simplifies to √(2) + 2√(2) = 3√(2).

Front

What is the difference between rational and irrational numbers?

Back

Rational numbers can be expressed as a fraction of two integers, while irrational numbers cannot be expressed as such, and their decimal representation is non-repeating and non-terminating.

Front

How do you rationalize the denominator of 1/√(3)?

Back

To rationalize the denominator, multiply the numerator and denominator by √(3): (1/√(3)) * (√(3)/√(3)) = √(3)/3.