Radical Operations Page 2
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1
25
[5
5 . [5
[5
2.JS • .J5
=
Z:S
=
2
11. Explain why
f5
was chosen as the number
by which to multiply.
12. Divide.
3
24
a.
2
../6
b.
../6
3ff0
c.
5D
5.f3
d. 3ff0
Using the fact that
,fci •
fh
=
.fOb,
we can
write
f63
as
ill · f3.
We can also write it as
{9 ·
.f7, which is especially convenient because
9 is a perfect square. Therefore:
[63
=
{9 . .fj
=
3.f7.
This last expression is in simplest radical form.
13. Write in simple radical form.
a.
hoo
b. ~ 147
c.
hoo
d. h75
14. Use dot paper to illustrate the addition
rs
+
zrs.
15. Using the figure you made in problem 14,
explain how to decide which of the two
equations
f5 +
no
=
n5
and
rs
+
no
=
{45 is correct.
16. Check your answer to problem 15 with a
calculator.
17 . .... True or False? Explain.
a.
16
+
9
=
25
b. ~16
+
9
=ill
c.
fi6
+
{9
= ill
d.
fi6
+
{9
= ~~16~+-cc9
18 . .... If a and b are positive numbers, is it
always, sometimes, or never true that
{;i
+
[b
=~a
+
b? Explain, with
examples.
The figure shows a right triangle, a square
having area a, a square having area b, and a
third square.
a
b
19. In terms of a and b,
a. what is the area of the third square?
Explain.
b. What are the sides of the triangle?
20 ..... If a and b are positive numbers, is
it always, sometimes, or never true that
{;i
+
fb
>
~a
+
b? Explain, using
the figure.
As you see, sums of radical expressions cannot
usually be simplified. However, in some cases,
simple radical form can help.
21. Simplify, then add or subtract.
a.m+m
b.
m-
4no
c.
f6o-
~ 135
d.
{45
+
h25
You can add or subtract square roots only if
they are the roots of the same number. This is
similar to combining like terms when adding
polynomials.
22. Simplify, then add or subtract, if possible.
a. 5
+
sf68
+
m
b. 6 - 6ill
+
{96
c.
rs
+
m
+
m -
M4
d.
m
+
no-
f36
+
M0- 60
Chapter 9 _Measurement and Square Roots
~~~~~~
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