Radicals & Simplifying Radical Expression

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.

Front

What does it mean to simplify a radical expression?

Back

To simplify a radical expression means to rewrite it in a simpler form, often by removing any perfect square factors from under the radical.

Front

How do you simplify the expression \( \frac{8}{\sqrt{6}} \)?

Back

Multiply the numerator and denominator by \( \sqrt{6} \) to get \( \frac{8\sqrt{6}}{6} = \frac{4\sqrt{6}}{3} \).

Front

What is the process of rationalizing the denominator?

Back

Rationalizing the denominator involves eliminating any radicals from the denominator of a fraction.

Front

How do you rationalize the denominator of \( \frac{\sqrt{5}}{2\sqrt{3}} \)?

Back

Multiply the numerator and denominator by \( \sqrt{3} \) to get \( \frac{\sqrt{15}}{6} \).

Front

What is the square root of a number?

Back

The square root of a number \( x \) is a value \( y \) such that \( y^2 = x \).

Front

What is the square root symbol called?

Back

The square root symbol is called a radical.

Front

What is a perfect square?

Back

A perfect square is an integer that is the square of another integer.

Front

How do you identify perfect square factors in a radical?

Back

To identify perfect square factors, look for factors of the number under the radical that can be expressed as the square of an integer.

Front

What is the simplified form of \( \sqrt{50} \)?

Back

The simplified form of \( \sqrt{50} \) is \( 5\sqrt{2} \) because \( 50 = 25 \times 2 \) and \( \sqrt{25} = 5 \).