Irrational Numbers and Roots

Front

What is an irrational number?

Back

An irrational number is a number that cannot be expressed as a fraction of two integers. Its decimal representation is non-repeating and non-terminating.

Front

What is a rational number?

Back

A rational number is any number that can be expressed as a fraction a/b, where a and b are integers and b is not zero.

Front

Is √2 a rational number?

Back

No, √2 is an irrational number.

Front

What is the square root of 16?

Back

The square root of 16 is 4, which is a rational number.

Front

If x³ = 125, what is the value of x?

Back

x = 5.

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): c² = a² + b².

Front

Using the Pythagorean Theorem, if the legs of a right triangle are 3 and 4 units, what is the length of the hypotenuse?

Back

The hypotenuse is 5 units.

Front

What is √50 approximately equal to?

Back

√50 is approximately equal to 7.1.

Front

In a right triangle, if one leg is 5 feet and the hypotenuse is 13 feet, how high does the other leg reach?

Back

The other leg reaches 12 feet.

Front

What is the approximate value of π?

Back

The approximate value of π is 3.14.