Simplifying Radical Expressions

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 simplify a square root?

Back

To simplify a square root, factor the number under the root into its prime factors and look for pairs of factors. For example, √18 = √(9*2) = 3√2.

Front

What is the square root of a product?

Back

The square root of a product is the product of the square roots. For example, √(ab) = √a * √b.

Front

What is the square root of a quotient?

Back

The square root of a quotient is the quotient of the square roots. For example, √(a/b) = √a / √b.

Front

How do you simplify √(x^2)?

Back

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

Front

What is the principle of simplifying radicals?

Back

The principle of simplifying radicals involves expressing the radical in its simplest form by removing perfect squares from under the radical.

Front

How do you simplify √(a^2b)?

Back

√(a^2b) simplifies to a√b, assuming a is non-negative.

Front

What is a perfect square?

Back

A perfect square is a number that can be expressed as the square of an integer. For example, 1, 4, 9, 16 are perfect squares.

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 a simple fraction. For example, √2 is irrational.

Front

How do you handle negative numbers under a square root?

Back

The square root of a negative number is not a real number; it is an imaginary number. For example, √(-1) = i.