Square Roots, Cube Roots and Pythagorean Theorem

Front

What is a square root?

Back

A square root of a number is a value that, when multiplied by itself, gives the original number. For example, √9 = 3 because 3 x 3 = 9.

Front

What is a cube root?

Back

A cube root of a number is a value that, when multiplied by itself three times, gives the original number. For example, ∛27 = 3 because 3 x 3 x 3 = 27.

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It is expressed as: a² + b² = c².

Front

Identify the hypotenuse in a right triangle with sides 5, 12, and 13.

Back

The hypotenuse is 13, as it is the longest side of the triangle.

Front

What is the square root of 144?

Back

12, because 12 x 12 = 144.

Front

What is 3 cubed?

Back

27, because 3 x 3 x 3 = 27.

Front

Which triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

Front

What is the relationship between squaring a number and finding its square root?

Back

Squaring a number is the process of multiplying the number by itself, while finding the square root is determining what number multiplied by itself gives the original number.

Front

If a triangle has sides of lengths 8, 15, and 17, is it a right triangle?

Back

Yes, because 8² + 15² = 64 + 225 = 289, which is 17².

Front

What is the square root of 25?

Back

5, because 5 x 5 = 25.