# Irrational Numbers

Click on the image at right to get the lesson app with instructor notes. Or you can install right from here by clicking the logo below: Students identify the square roots of perfect square integers as rational numbers and the square roots of non-perfect-square integers as irrational numbers, which are numbers that cannot be represented as a ratio of two integers. Students estimate the decimal values of irrational numbers as square roots and estimate the locations of these irrational numbers on a number line.

In the second module, students use the equation from the Pythagorean Theorem to calculate or estimate the hypotenuse length of right triangles given the leg lengths. Students also use square roots to determine the side lengths of squares given their areas.

Finally, students determine the square roots of fractions with numerators and denominators that are perfect squares and determine the square roots of decimals by rewriting the decimals as ratios of perfect-square values. Students also compare square root expressions.

Module 1 Video

This video introduces students to the square root of 2 via the formula a2 + b2 = c2 from the Pythagorean Theorem and to the concept of irrational numbers, which can’t be represented as the ratio of two integers.