Simplifying Radicals

Front

What is a radical in mathematics?

Back

A radical is a symbol used to indicate the root of a number, most commonly the square root. It is represented by the radical sign (√).

Front

How do you simplify a radical expression?

Back

To simplify a radical expression, factor the number under the radical into its prime factors, and then look for pairs of factors to take out of the radical.

Front

What is the square root of 16?

Back

The square root of 16 is 4.

Front

What is the simplified form of √a²?

Back

The simplified form of √a² is |a|, where |a| denotes the absolute value of a.

Front

How do you simplify √(ab)?

Back

√(ab) can be simplified to √a * √b, provided that a and b are non-negative.

Front

What is the simplified form of √(x²y)?

Back

The simplified form of √(x²y) is x√y, assuming x is non-negative.

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

What is the quotient property of square roots?

Back

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

Front

How do you simplify 4√75?

Back

4√75 simplifies to 20√3.

Front

What is the simplified form of √140?

Back

The simplified form of √140 is 2√35.