Radical Operations

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lESSON
Radical Operations
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1.
l@i[.lbiii·hi
Using only multiplication,
write at least three radical expressions that
equal each of the following.
a.
2f3
b. 6
Even though you are often asked to simplify
expressions, it is sometimes just as important
to know how to "complicate" them. For
example, 3fi is equivalent to all these radical
expressions.
f9fi
f3f3fi
2. Write at least two other radical expressions
equivalent to:
a.
5/2;
c.
6110;
b. 2I5;
d. !OM.
3. Write each as the square root of a number.
(For example, 3fi
=
f6:i .)
a.
2/2
b. 2fi
c.
5M
d. 4f3
4. Write each as the product of as many
square roots as possible.
(For example,
3M
=
f3 · f3 · fi · f3.)
a. 5ffil
b. 7I5
c.
f30
d.
10m
5. What number times
M
equals 3ffiJ'>
To answer problem 5, Tina wrote:
. M
=
3ffil
. f3fi
=
f3f3fi{5
9.4 Radical
"First I wrote everything as a product of
square roots," she explained. 'Then it was easy
to see that the missing factors were {5 and f3,
so the answer must be
ill."
Erin politely told Tina that her method seemed
unnecessarily complicated. Erin wrote:
. M
=
3fi0
. M
=
[9[10
. M
=
J9o
"My goal was to write 3 ffil as the square root
of something. Once I found that 3[10
=
J9o,
it was easy from there. I could use the rule that
,Ja · fb
=
.r;;b
to see that the answer was
ill,"
she explained.
6. What number times 2fi0 equals 10!2?
Find the answer by using
a. Tina's method;
b. Erin's method.
7. What num her times
18
equals 4?
8. What number times 2!2 equals 4f3
7
9. Divide 5 by
2IS.
"That's not fair," said Tina. "Ms. Kern never
taught us to divide with radicals." 'That's
true," said Erin, "but we know that
multiplication and division are inverse opera-
tions." She wrote:
· 2IS
=
5
. {4{5
=ill
10. Finish solving the problem using Erin's
method.
Another way to solve this problem is to use the
following trick: Write an equivalent fraction
without a square root in the denominator. In
this case, we multiply both the numerator and
denominator by
f5.

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