Estimating Square Roots: Techniques and Strategies

The video tutorial explains how to estimate the square root of a non-perfect square, specifically focusing on the square root of 15. It begins by identifying perfect squares close to 15, such as 9 and 16, and uses these to narrow down the range of possible values. The tutorial then demonstrates how to refine the estimate using a number line and calculations, ultimately concluding that 3.9 is a good approximation for the square root of 15. The process involves a divide and conquer approach, making educated guesses and verifying them through calculations.

Why is working with square roots considered tricky?

• Because they cannot be estimated.

• Because they are always irrational numbers.

• Because they often involve complex algebraic steps.

• Because they always result in whole numbers.

What is the first step in estimating the square root of 15?

• Using the square root of 10 as a reference.

• Finding the exact value using a calculator.

• Identifying whole numbers close to the square root of 15.

• Guessing a random number.

Which perfect square is smaller than 15?

• 16

• 9

• 4

• 25

Which perfect square is larger than 15?

• 9

• 12

• 20

• 16

What is the approximate range for the square root of 15?

• Between 3 and 4

• Between 5 and 6

• Between 2 and 3

• Between 4 and 5

Why is the square root of 15 closer to 4 than to 3?

• Because 15 is closer to 16 than to 9.

• Because 15 is closer to 9 than to 16.

• Because 15 is an even number.

• Because 15 is a prime number.

What was the first guess for the square root of 15?

• 3.9

• 3.8

• 3.7

• 4.0

What was the result of squaring 3.9?

• 15.00

• 14.44

• 15.21

• 16.00

What was the result of squaring 3.8?

• 16.00

• 15.21

• 14.44

• 15.00

What is the final estimate for the square root of 15?

• 3.7

• 4.0

• 3.8

• 3.9