Multiplying Radicals

Front

Define a radical.

Back

A radical is a symbol used to indicate the root of a number, most commonly the square root.

Front

What is the product of two radicals with the same index?

Back

The product of two radicals with the same index can be simplified by multiplying the numbers inside the radicals together.

Front

Simplify: √a ⋅ √b

Back

√(a*b) - The product of two square roots is the square root of the product.

Front

What is the square root of 36?

Back

6 - The square root of 36 is the number that, when multiplied by itself, gives 36.

Front

Simplify: 2√3 ⋅ 4√5

Back

8√15 - Multiply the coefficients (2 and 4) and the radicands (3 and 5) together.

Front

What is the index of a radical?

Back

The index of a radical indicates the degree of the root being taken, such as square root (index 2) or cube root (index 3).

Front

Simplify: 3√2 + 5√2

Back

8√2 - Like terms can be combined by adding their coefficients.

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.

Front

Simplify: √(x^2)

Back

|x| - The square root of a variable squared is the absolute value of that variable.

Front

What is the product of √a and √a?

Back

a - The product of a square root with itself returns the original number.