Perfect Squares that are Written as Fractions or Decimals

Size: px

Start display at page:

Download "Perfect Squares that are Written as Fractions or Decimals"

Amber McDaniel
5 years ago
Views:

1 Math 9: Unit 1 Lesson 2 Perfect Squares that are Written as Fractions or Decimals Part 1: Fractions There are two ways to determine the square root of a perfect square that is written as a fraction: 1. Algebraically 2. Using a diagram (square) Algebraic Method: Steps If the number is written as a mixed number, change it to an improper fraction. Reduce the fraction to lowest terms (if possible). Take the square root of the numerator and denominator. Examples: Determine the square root of each fraction. (A) 1

2 (B) Hint: You must change mixed numbers to improper fractions before finding the square root. (C) Hint: You must reduce fractions (if possible) before finding the square root. 2

3 Diagram Method Steps: Draw a larger square made of smaller squares (the number of smaller squares will be the denominator of the fraction). Starting at the top left corner of the larger square, shade in some of the smaller squares (shade in a number of squares equal to the numerator). Determine the square root by reading off the side length. Example: Use a diagram to determine the square root of Example: Use a diagram to determine the square root of 9/25. 3

4 Finding the Square Root of a Perfect Square Fraction in Decimal Form If we are asked to determine the square root of a perfect square fraction, and are expected to write the answer as a decimal, we can simply use our calculator to determine the answer. Example: Determine the square root of in decimal form. Part 2: Decimals If we are asked to find the square root of a perfect square decimal number, we may either have to write the answer in decimal form or as a fraction. Example: Determine the square root of in decimal form using a calculator. 4

5 If we are expected to write the square root of a perfect square decimal number in fraction form, we must first change the decimal number to a fraction... Once we rewrite the decimal as a fraction, we can find the square root the same way we did for fractions. 5

6 Example: Determine the square root of Write the answer as a fraction. Calculating a Number Whose Square Root is Given Rule: Square the square root of the number to get the value. Examples: Calculate the number whose square root is... (A) 4.5 (B) 4/5 Textbook Questions: p # 3(write these answers in fraction form), 5, 7, 9, 13, 14 For # 5 and 7, if the perfect square is a decimal, write its square root in decimal form. If the perfect square is a fraction, write its square root in fraction form. 6

7 Determining Whether Given Numbers are Perfect Squares All of the numbers that we have attempted to take of square root of so far have been perfect squares. However, not all numbers are perfect squares. Here, we will learn to determine whether or not fractions and decimals are perfect squares. Fractions To determine whether a fraction is a perfect square, follow the process that we used earlier to determine the perfect square of the fraction. If the fraction is reduced and we CANNOT take the square root of the numerator or denominator or both, then the fraction is NOT a perfect square. Examples: Determine whether the following are perfect squares. (A) (B) 7

8 Decimals To determine whether a decimal number is a perfect square, take the square root of the number using a calculator. If either of the following conditions are met, then the decimal is a perfect square... it terminates (ends after a certain number of decimal places) or it repeats (has a repeating pattern of digits in the decimal). Example: Complete the following table... 8

9 Textbook Questions: p. 11 #8 9

Square Roots of Perfect Squares. How to change a decimal to a fraction (review)

$Square Roots of Perfect Squares. How to change a decimal to a fraction (review)$ Section 1.1 Square Roots of Perfect Squares How to change a decimal to a fraction (review) A) 0.6 The 6 is in the first decimal position called the tenths place. Therefore, B) 0.08 The 8 is in the second