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# Square Roots and Irrational Numbers

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by

Tweet## Tim Franklin

on 26 November 2012#### Transcript of Square Roots and Irrational Numbers

What's the area of this square? REMEMBER: Square Roots and IRRATIONAL Numbers 4 ft RATIONAL numbers can be written as a ratio of two integers.

As decimals, they either terminate (end) or repeat. TO RECAP: Square roots are the inverses of squares. So what's an IRRATIONAL number? An IRRATIONAL NUMBER has a decimal form that neither terminates (ends) nor repeats. 4 x 4 = 16 sq ft Okay, this one? 1 ft 1 x 1 = 1 sq ft The square of an integer is called a PERFECT SQUARE. 5 2 = 25 What's the side length of this square? Area = 25 sq ft 5 x 5 = 25 sq ft Okay, this one? 3 ft 3 x 3 = 9 sq ft The inverse of squaring a number is finding a square root. 5 ft 5 ft 5 ft 5 ft Area = 9 sq ft 3 ft 3 ft 3 ft 25 = 5 FOR EXAMPLE: 1

2 = 0.5 2

3 = 0.6666... = 0.6 7

8 = 0.875 One example is the number , or pi, which neither ends nor repeats - 5 trillion digits and counting! ALSO: If an integer is not a perfect square, its square root is irrational. 13 Irrational numbers (as decimals) do not end or repeat. The square roots of non-perfect squares are

Irrational Numbers. We can find between which two integers the square root of a non-perfect square lies. So where is ? 13

Full transcriptAs decimals, they either terminate (end) or repeat. TO RECAP: Square roots are the inverses of squares. So what's an IRRATIONAL number? An IRRATIONAL NUMBER has a decimal form that neither terminates (ends) nor repeats. 4 x 4 = 16 sq ft Okay, this one? 1 ft 1 x 1 = 1 sq ft The square of an integer is called a PERFECT SQUARE. 5 2 = 25 What's the side length of this square? Area = 25 sq ft 5 x 5 = 25 sq ft Okay, this one? 3 ft 3 x 3 = 9 sq ft The inverse of squaring a number is finding a square root. 5 ft 5 ft 5 ft 5 ft Area = 9 sq ft 3 ft 3 ft 3 ft 25 = 5 FOR EXAMPLE: 1

2 = 0.5 2

3 = 0.6666... = 0.6 7

8 = 0.875 One example is the number , or pi, which neither ends nor repeats - 5 trillion digits and counting! ALSO: If an integer is not a perfect square, its square root is irrational. 13 Irrational numbers (as decimals) do not end or repeat. The square roots of non-perfect squares are

Irrational Numbers. We can find between which two integers the square root of a non-perfect square lies. So where is ? 13