Square and Cube Roots

Front

What is the definition of a square root?

Back

A square root of a number x is a number y such that y² = x. For example, √9 = 3 because 3² = 9.

Front

What is the definition of a cube root?

Back

A cube root of a number x is a number y such that y³ = x. For example, ∛27 = 3 because 3³ = 27.

Front

What is the approximate value of √20?

Back

√20 is approximately 4.47, which lies between the integers 4 and 5.

Front

How do you find the side length of a cube given its volume?

Back

To find the side length of a cube, take the cube root of the volume. For example, if the volume is 1,000 cm³, the side length is ∛1000 = 10 cm.

Front

If a square has an area of 32 square inches, how do you find the side length?

Back

To find the side length of a square, take the square root of the area. √32 is approximately 5.66, which lies between 5 and 6.

Front

What is the square root of a negative number?

Back

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

Front

What is the value of –√25?

Back

–√25 = -5, since the square root of 25 is 5.

Front

How can you determine if a number is a perfect square?

Back

A number is a perfect square if its square root is an integer. For example, 16 is a perfect square because √16 = 4.

Front

What is the relationship between square roots and exponents?

Back

The square root of a number can be expressed as an exponent: √x = x^(1/2).

Front

What is the relationship between cube roots and exponents?

Back

The cube root of a number can be expressed as an exponent: ∛x = x^(1/3).