COURSE 3 LESSON 4-8
Exploring Square Roots and Irrational Numbers
Find the two square roots of each number.
1
a. 81
b. 36
9 • 9 = 81
1
1
1
•
=
6
6
36
–9 • (–9) = 81
1
– 6 •
The two square roots of 81
are 9 and –9.
1
1
–6
= 36
The two square roots of
are 1 and – 1 .
6
4-8
6
1
36
COURSE 3 LESSON 4-8
Exploring Square Roots and Irrational Numbers
Estimate the value of –
70 to the nearest integer.
Since 70 is closer to 64 than it is to 81, –
4-8
70
–8.
COURSE 3 LESSON 4-8
Exploring Square Roots and Irrational Numbers
The math class drops a small ball from the top of a stairwell.
They measure the distance to the basement as 48 feet. Use the
formula d = 16t2 to find how long it takes the ball to fall.
d = 16t2
Use the formula.
48 = 16t2
Substitute 48 for d.
48
2
=
t
16
Divide each side by 16.
3 = t2
Simplify.
4-8
COURSE 3 LESSON 4-8
Exploring Square Roots and Irrational Numbers
(continued)
3=t
Find the positive square root.
3
1.7
1.7320508
Use a calculator.
t
Round to the nearest tenth.
It takes about 1.7 seconds for the ball to fall 48 ft.
4-8
COURSE 3 LESSON 4-8
Exploring Square Roots and Irrational Numbers
Identify each number as rational or irrational. Explain.
a. –9.3333
7
Rational; the decimal repeats.
43
b. 4 9
Rational; the number can be written as the ratio 9 .
c.
Irrational; 90 is not a perfect square.
90
d. 6.36366366636666. . .
Irrational; the decimal does not terminate
or repeat.
4-8
COURSE 3 LESSON 4-8
Exploring Square Roots and Irrational Numbers
1. Find the two square roots of 400.
20 and –20
2. Estimate
34 to the nearest integer.
6
3. Using d = 16t 2, find how long it takes a skydiver to fall 676 ft from
an airplane.
6.5 s
64 rational or irrational? Explain.
5
Rational; it can be written as 8 .
5
4. Is
4-8