Virginia SOL Math / Grade 8 / Number & Number Sense

8.NS.1

Compare & Order Real Numbers

What you'll learn

  • Estimate and compare the values of square roots and other real numbers
  • Order a set of real numbers written in different forms
  • Locate real numbers on a number line

Words to know

Real number —
any rational or irrational number
Square root —
a number that multiplies by itself to give another number
Perfect square —
a number whose square root is a whole number, like 49
Irrational number —
a number whose decimal never ends or repeats, like the square root of 2
Number line —
a line on which every real number has a point

Why it matters Comparing real numbers lets us order measurements, prices, and data even when some are fractions, decimals, or roots that are not exact.

Worked examples

Model ItI do

Order from least to greatest: the square root of 20, 4.5, and 9/2.

The square root of 20 is between the square root of 16 (which is 4) and the square root of 25 (which is 5), close to 4.47. Note 9/2 equals 4.5. So the order is the square root of 20, then 4.5 = 9/2 (a tie), giving square root of 20 < 4.5 = 9/2.

Try It TogetherWe do

Write >, <, or = : the square root of 50 ___ 7.

Since 7 times 7 equals 49 and the square root of 49 is 7, the square root of 50 is a little more than 7. So the square root of 50 > 7.

Now YouYou do

Order from greatest to least: 3.8, the square root of 15, and 15/4.

Estimate the square root of 15 and convert 15/4 to a decimal, then compare. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Which is greater: 3 or the square root of 4?

  2. 2.Write >, <, or = : the square root of 25 ___ 5

  3. 3.Between which two consecutive whole numbers is the square root of 10?

On Level

The core Quick Check from the book.

  1. 1.Write >, <, or = : the square root of 30 ___ 6

  2. 2.Between which two consecutive whole numbers is the square root of 40?

  3. 3.Order from least to greatest: 2.5, the square root of 9, 5/2.

  4. 4.Is the square root of 2 rational or irrational?

  5. 5.Which is greater: the square root of 80 or 9?

Challenge

Stretch your thinking.

  1. 1.Order from least to greatest: the square root of 45, 6.5, and 20/3.

  2. 2.Between which two consecutive whole numbers does the square root of 155 fall, and which is it closer to?

  3. 3.A number line shows -3, and points A and B. If A is at the square root of 2 and B is at 7/4, which point is farther right?