Comparing and Ordering Real Numbers

The video tutorial covers the comparison and ordering of rational and irrational numbers, focusing on square roots. It begins with a review of previous lessons on rational and irrational numbers and fractions. The teacher explains how to compare square roots without a calculator by squaring numbers. The tutorial also addresses handling negative square roots and their comparisons. It demonstrates ordering numbers from least to greatest and greatest to least using square roots, emphasizing the importance of understanding the relationship between numbers and their square roots.

What is the first step in comparing square roots without a calculator?

• Use a table

• Estimate the values

• Square the numbers

• Find the decimal values

How do you compare the square root of 9 and the square root of 12?

• By using a calculator

• By finding their decimal values

• By squaring both numbers

• By estimating their values

When comparing fractions, what should you do with the numerator and denominator?

• Add them

• Subtract them

• Square them

• Divide them

What is the square of 2.6?

• 7.84

• 6.76

• 5.76

• 8.64

Why is the negative square root of 7 less than the negative square root of 6.76?

• Because 6.76 is a smaller number

• Because 7 is less than 6.76

• Because negative numbers are always smaller

• Because the larger the negative number, the smaller it is

What is the square root of 2.56?

• 1.8

• 2.6

• 2.8

• 1.6

Which of the following is the smallest when ordered from least to greatest?

• Square root of 7.84

• Square root of 2

• Square root of 2.56

• Square root of 4

What is the square of 1.7?

• 3.89

• 1.89

• 4.89

• 2.89

How do you convert 5/3 into a comparable form for square roots?

• By dividing 5 by 3

• By squaring both the numerator and denominator

• By subtracting 3 from 5

• By adding 5 and 3

Which of the following is the largest when ordered from greatest to least?

• Square root of 2.89

• Square root of 2.7

• Square root of 9

• Square root of 3