Page 85 - Algebra 1

Not all numbers are perfect squares, but their square roots can be estimated.
Example
2
Estimating Square Roots
Estimate the value √5 0 to the nearest integer. Explain your reasoning. SOLUTION
√5 0 is not a perfect square.
Determine which two perfect squares 50 falls between on the number line. 50 is between the perfect squares 49 and 64.
Then determine which perfect square √5 0 is closest to.
√5 0 is between the numbers 7 and 8 because √4 9 = 7 and √6 4 = 8. √5 0 is closer to the number 7 because 50 is closer to 49 than 64.
Math Reasoning
Analyze Is 1.44 a perfect square?
√ 5 0 ≈ 7
√49 √50 √64
5678
When comparing expressions that contain radicals, simplify the expressions with radicals first. Next, perform any operations necessary. Then compare the expressions.
Comparing Expressions Involving Square Roots
Compare the expressions. Use <, >, or =.
√ 4 + √ 36 √ 9 + √ 25
SOLUTION
√ 4 + √ 36 √ 9 + √ 25
2 + 6 3 + 5 Simplify the expressions.
8=8 Add.
Application: Ballroom Dancing
The area of a dance floor that is in the shape of a square is 289 square feet. What is the side length of the dance floor? Explain.
SOLUTION
The side length can be found by finding the square root of the area. Area of a square = side length × side length
Example
3
Caution
Square roots must be simplified before performing any other operations. For example, √4 + √ 36 ≠ √ 40.
Example
4
70 Saxon Algebra 1
A = s2 289 = s2
√ 28 9 = s 17 = s
Write the formula. Substitute 289 for A.
Find the square root of 289.
Each side length of the dance floor is 17 feet.