Estimating Roots

Lesson 1-9

Real World Link

ESTIMATING SQUARE ROOTS TO THE NEAREST TENTH

Once you have found which two whole numbers your square root is between, you must estimate your square root to the nearest tenth.•Decide which whole number your original number is closest to.•Test the square root tenths to find the nearest square to your original number.Example: Estimate √83 to the nearest tenth.

In example 1 we estimated that √83 is between 9 and 10

Since 83 is closer to 81 than 100, we can test tenths close to 9. (9.1)² = 82.81 83.00 – 82.81 = 0.19 (9.2)² = 84.64 84.64 – 83.00 = 1.64

Since (9.1)² is closer to 83, √83 is estimated as 9.1 √83 ≈ 9.2

ESTIMATE TO THE NEAREST TENTH

EXAMPLE

ORDERING NUMBERS To order a set of numbers that include square

roots, you must first estimate the decimal equivalent of the square roots.

Then order the numbers Finally, write the numbers in their original

form. Example: Order the set {7, 9, √50, √85}. 1. Estimate the square roots {7, 9, 7.1, 9.2}

2. Order the decimals {7, 7.1, 9, 9.2} 3. Rewrite in original form {7, √50, 9, √85}

TRY THESE Estimate to the nearest tenth.

p 85 #1-31 odd, 32-38 all

HOMEWORK