Estimating Square Roots by Comparing to Perfect Squares

This lesson teaches how to estimate the value of square roots by comparing them to perfect squares. It explains the concept of irrational numbers and demonstrates the estimation process using the square root of 32 as an example. The lesson covers finding perfect squares on either side of the target number, using a number line for refinement, and alternative estimation methods. Practical applications of these estimation techniques are also discussed, emphasizing the importance of understanding square roots without relying solely on calculators.

What is an irrational number?

• A number that is always a whole number

• A number that can be expressed as a fraction

• A number with a repeating decimal

• A number that cannot be expressed as a ratio of integers

Which two perfect squares are used to estimate the square root of 32?

• 36 and 49

• 16 and 25

• 25 and 36

• 9 and 16

What is the approximate value of the square root of 32 based on the number line method?

• 5.7

• 5.6

• 5.8

• 5.5

Why is it useful to know perfect squares when estimating square roots?

• To quickly identify numbers between which the square root lies

• To avoid using a calculator

• To solve all mathematical problems

• To memorize all square roots

What is a practical example of estimating square roots without a calculator?

• Finding the length of a rope at a store

• Measuring the height of a building

• Calculating the area of a circle

• Solving a quadratic equation