Evaluating Algebraic Expressions 4-7 Estimating Square Roots NS2.4 Use the inverse relationship between raising to a power and extracting the root of a perfect square integer; for an integer that is not a square, determine without a calculator the two integers between which its square root lies and explain why. California Standards

Evaluating Algebraic Expressions 4-7 Estimating Square Roots Additional Example 1: Estimating Square Roots of Numbers The 55 is between two integers. Name the integers. Explain your answer. List perfect squares near 55.36, 49, 64, < 55 < 64 Find the square roots of the perfect squares is between 7 and 8 because 55 is between 49 and 64. Find the perfect squares nearest < 55 < 64 7 < 55 < 8

Evaluating Algebraic Expressions 4-7 Estimating Square Roots Check It Out! Example 1 List perfect squares near 80.49, 64, 81, < 80 < 81 Find the square roots of the perfect squares is between 8 and 9 because 80 is between 64 and 81. The 80 is between two integers. Name the integers. Explain your answer. Find the perfect squares nearest < 80 < 81 8 < 80 < 9

Evaluating Algebraic Expressions 4-7 Estimating Square Roots A Coast Guard boat searching for a lost sailboat covers a square area of 185 mi 2. What is the approximate length of each side of the square area? Round your answer to the nearest mile. Additional Example 2: Recreation Application 169 < 185 < 196 Find the perfect squares nearest 185. Find the square roots of the perfect squares. Each side of the search area is about 14 miles long. The length of each side of the square is √185. < < √185√169 √ < < 14√185 √185  , 169, 196, 225 List perfect squares near is closer to 196 than to 169, so 185 is closer to 14 than 13.

Evaluating Algebraic Expressions 4-7 Estimating Square Roots Check It Out! Example 2 A tent was advertised in the newspaper as having an enclosed square area of 168 ft 2. What is the approximate length of the sides of the square area? Round your answer to the nearest foot. The length of each side of the square is √ < 168 < 169Find the perfect squares nearest 168. Find the square roots of the perfect squares. < < √168√144 √ < < 13√16 8 √168  13 Each side of the tent is about 13 feet long. 121, 144, 169, 196 List perfect squares near is closer to 169 than to 144, so 168 is closer to 13 than 12.