6th Grade Math Textbook, Fundamentals

 &KDSWHU

10-4

Irrational Numbers

Objective To distinguish rational and irrational numbers • To approximate the square root

of a number that is not a perfect square •To locate irrational numbers on a number line

A square region of farmland has an area of

44 square kilometers. What is the length of each

side of the region of land? Round the length to

the nearest tenth of a kilometer.

The length of a side of a square with an area of 44 km^2

is. Use this idea to solve the problem.

You can use estimation to approximate numbers such as

. To estimate the square root of a number that is not
a perfect square, consider the perfect squares just before
and just after the number under the radical sign.
To estimate , identify the perfect
squares that 44 is between.
Compare these as inequalities.
Take the square root of the numbers, and
evaluate the perfect squares.

So is between 6 and 7. It is closer to 7 than to 6.

You can use the square root key on your calculator to find a better estimate.

Press 4 4

This tells you that is a little more than 6.6.

You can locate numbers such as on a number line.

So the length of each side of the square region of farmland is about 6.6 kilometers.

√ 36 √ 44 √ 49

6.5 7.06.8 6.96.76.66.46.2 6.36.16.0

44

44

6.633249581

44

44

44

44

44 is between 36 and 49.

36  44  49



6   44 7

36 44 49

Approximate to the nearest whole number.

Identify the perfect  

squares closest to.

Find the positive

square roots of the 4   5

perfect squares.

Since 23 is closer to 25 than to 16, to the

nearest whole number is about 5.

23

23

23

252316

(^123) Approximate to the nearest tenth.
Press 3 1
Round the answer to the nearest tenth.
5.567764363 5.6
The square root of 31 rounded to the
nearest tenth is 5.6.
5.567764363
(^231)