How to Approximate Square Roots Without a Calculator

This video tutorial teaches how to estimate square roots of non-perfect squares. It covers identifying non-perfect squares, using a number line to find integer bounds, and estimating square roots to the nearest hundredth. The video explains the properties of non-perfect squares, such as being irrational and non-repeating, and introduces a pattern in the number of non-perfect squares between perfect squares. It also provides a step-by-step method to estimate square roots without a calculator, using a ratio and rounding technique.

What is the main objective of today's lesson?

• To understand linear functions

• To solve quadratic equations

• To estimate square roots

• To learn how to multiply integers

Which of the following is a characteristic of non-perfect squares?

• They are always integers

• They are non-terminating and non-repeating decimals

• They are terminating decimals

• They are rational numbers

How many non-perfect squares are there between the perfect squares 4 and 9?

• Two

• Three

• Four

• Five

Which of the following is true about the pattern of non-perfect squares between perfect squares?

• The number of non-perfect squares increases by 2 each interval

• The number of non-perfect squares decreases by 2 each interval

• The number of non-perfect squares is always 5

• The number of non-perfect squares remains constant

What is the first step in estimating a square root to the nearest hundredth?

• Divide the radicand by 2

• Identify the two consecutive integers it lies between

• Multiply the radicand by itself

• Subtract the radicand from 100

Which of the following is the correct ratio setup for estimating sqrt(19)?

• (19 - 1) / (25 - 1)

• (19 - 9) / (25 - 9)

• (19 - 4) / (25 - 4)

• (19 - 16) / (25 - 16)

What is the estimated value of sqrt(19) to the nearest hundredth?

• 4.35

• 4.31

• 4.33

• 4.37

Which two integers does sqrt(47) lie between?

• 5 and 6

• 8 and 9

• 7 and 8

• 6 and 7

What is the estimated value of sqrt(47) to the nearest hundredth?

• 6.87

• 6.85

• 6.83

• 6.81

What is the estimated value of -sqrt(18) to the nearest hundredth?

• -4.22

• -4.26

• -4.20

• -4.24