Question

Simplify radical 64.

Answer 1

8

Answer 2

since
\[8^2=64\]

Answer 3

Simplifying and solving are two different things, isnt it?

Answer 4

\[64=8^2\]So\[\sqrt{64} = \sqrt{8^2} = 8\]

Solving generally requires an equation with one or more variables.

Answer 5

simplifying just means 'rewrite' in the form I want.

Answer 6

well unfortunately many math teachers use "simply" to mean all kinds of different things, confusing the hell out students

Answer 7

Where the form they're looking for isn't always clear.

Answer 8

there is no such math term as "simplify" it is pure laziness or confusion on their part

Answer 9

sometimes it just means compute

Answer 10

sometimes it means multiply
sometimes it means combine like terms
sometimes it means factor and cancel

you never know

Answer 11

nothing on earth is more confusing to use one term or one symbol to mean many different things. sheer utter laziness is what it is, usually from people who should not be teaching math or writing books

Answer 12

Tell me about it... hahah . I thought you had to do something like radical 2*2*2*2*2*2 and then pair the twos and then take them out, so you would get a normal 6 instead of a radical 8.. But i dont know what they mean by simplify. :l

Answer 13

there is such a thing as "simplest radical form" and it has specific rules
in this case you just have the square root of 64 which is pretty obviously 8.
only reason you thought twice was because some moron wrote "simplify"

Answer 14

You can certainly do that if you like:

\[64 = 2\times 2 \times 2 \times 2\times 2 \times 2\]So
\[\sqrt{64} = \sqrt{2\times 2 \times 2 \times 2\times 2 \times 2} = 2\times 2\times 2 = 8 \]

Answer 15

You take out a pair of 2's and it becomes 1 two after you take the square root.

Answer 16

But that seems too easy... I mean, its geomerty homework! Shouldnt it be all confusing and such? and ohh! i got it! i did my math wrong. It all does the same thing...

Answer 17

sure if you have infinite patience. i guess you could do that with
\[\sqrt{169}\] or
\[\sqrt{1,000,000}\] if you like

Answer 18

Mkay, so how do you multiply radicals?

Answer 19

Lol, no it should be easy. =)

Answer 20

\[\sqrt{a} \times \sqrt{b} = \sqrt{a\times b}\]

Answer 21

if the index is the same multiply the radicands. what polpak said

Answer 22

Oh.. okay. uh, what about radical 40? Cause that cant be squarre rooted like 64...

Answer 23

That's ok, it can still be factored.

Answer 24

into what?

Answer 25

\[40=4\times 10\]
\[\sqrt{40}=\sqrt{4\times 10}=\sqrt{4}\times \sqrt{10}=2\sqrt{10}\]

Answer 26

the it is in all gory details

Answer 27

Mkay, thats what i thought....

Answer 28

not too bad. factor the number and make sure to take out all perfect squares if it is a square root

Answer 29

8 times 8 is 64, so 8

Answer 30

what about dividing radicals?

Answer 31

same thing

Answer 32

How?

Answer 33

\[\sqrt{\frac{64}{49}}=\frac{8}{7}\] for example

Answer 34

\[40 = 4\times 10\]
\[\implies \sqrt{40} = \sqrt{4\times 10} = \sqrt{4}\times \sqrt{10}\]

Answer 35

bah, little late on that reply ;p

Answer 36

in other words
\[\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}\]

Answer 37

@polpak not as late as karatechopper!

Answer 38

So you can do each problem sepratley, and then then just put the line thing in between them and you have your answer?

Answer 39

hey hey hey i just logged on to openstudy! whats my fault in it?

Answer 40

well you have a choice. you can divide and take the square root second or take the square root separately and then divide. the equal sign means you get the same thing in either case

Answer 41

@karatechopper no offense meant. sorry

Answer 42

you have an example?

Answer 43

radical 120 over radical 10

Answer 44

so you can divide 120 by 10 to get 12 first

Answer 45

then you would have
\[\sqrt{12}\]

Answer 46

and since
\[12=4\times 3\] you get
\[\sqrt{12}=\sqrt{4\times 3}=2\sqrt{3}\]

Answer 47

apology exepted i will become ur fan can u become mine?

Answer 48

Mkay, that makes sense. What about if you have a problem like 3 radical 5 * 2 radical 10? what do you do to the numbers that arent in the radical?

Answer 49

make them the same

Answer 50

How?

Answer 51

\[\sqrt[3]{5}\sqrt{10}\] is that it?

Answer 52

Typically you'd do that with fractional exponents.

Answer 53

unfortunately you have to make them in to 6ht roots since that is the least common multiple of 2 and 3

Answer 54

Converting your radical into a fractional exponent.

Answer 55

for example
\[\sqrt{10}=\sqrt[6]{10^3}\]

Answer 56

and
\[\sqrt[3]{5}=\sqrt[6]{5^2}\]

Answer 57

so now that the indexes are the same you can combine them

Answer 58

... Im confused. why do you have to change them? Whats an index?

Answer 59

and get
\[\sqrt[6]{5^2\times 10^3}\]

Answer 60

ok lets to slow

Answer 61

Have you learned about fractional exponents and their relationship to radicals?

Answer 62

\[\sqrt{5} = 5^{\frac{1}{2}}\]

Answer 63

the index is the number outside the radical. so for example in
\[\sqrt[5]{x^8}\] the index is 5

Answer 64

this means the fifth root

Answer 65

in
\[\sqrt[3]{5}\] the index is 3. this means the cube root

Answer 66

if you do not see an index, for example in
\[\sqrt{5}\] the index is assumed to be 2

Answer 67

Uh... Probbably. I just dont remember anything. Math was my first class of the day, and you cant really learn much at 7 in the monring. And ... blah! this is still confusing. This is what my equation looks like.

Answer 68

^^number 5.

Answer 69

oh my dear. sorry for confusing you

Answer 70

this is not an index, this is just a number.

Answer 71

Thats what i thougght!(:

Answer 72

answer to number 5 is
\[6\sqrt{50}\]

Answer 73

easy easy easy

Answer 74

Is that simplified?

Answer 75

right?
\[2\times 3=6\]
\[5\times 10=50\]

Answer 76

no now we simplify.
\[50=25\times 2\] so
\[\sqrt{50}=5\sqrt{2}\]

Answer 77

because
\[\sqrt{50}=\sqrt{25\times 2}=5\sqrt{2}\]

Answer 78

so you get
\[6\times 5\times \sqrt{2}=30\sqrt{2}\]

Answer 79

Oh... Wait what about the 6? The final answer would be 30 radical 2 right?

Answer 80

\[6\sqrt{50} \]\[= 6 \times \sqrt{50}\]\[=6 \times \sqrt{5\times 5 \times 2}\]\[ = 6\times 5\times \sqrt{2}\]\[=30\sqrt{2}\]

Answer 81

Alright, it makes sense. Much easier than all that index jazz. (:

Answer 82

yes

Answer 83

i misread what you wrote. sorry

Answer 84

Yes, indexes will come later ;)

Answer 85

Not that they're harder, but you have to be able to do this well before you can do that well ;)

Answer 86

Hah, its alright . How do you subtract radicals? like... 3 radical 6 - 8 radical 6.?

Answer 87

You cannot. You have to make them products of similar factors, then factor out what's in common.

Answer 88

So \[3\sqrt{6} - 8\sqrt{6} = (3-8)\sqrt{6}\]

Answer 89

Actually this one you can think of like oranges. If you have 3 oranges and you subtract 8 oranges you will have how many oranges?

If you have 3 sqrt(6)s and you subtract 8 sqrt(6)s how many sqrt(6)s will you have left?

Answer 90

... uh. none?

Answer 91

You'll have -5

Answer 92

Ok, the oranges things breaks down a bit when talking about negative numbers, but you get the idea ;p

Answer 93

So... the answer is -5?

Answer 94

it's \[-5\sqrt{6}\]

Answer 95

If it helps you to think about it:
\[let\ a = \sqrt{6}\]
\[3\sqrt{6} - 8\sqrt{6} = 3a - 8a = -5a = -5 \sqrt{6}\]

Answer 96

Oh allright, thank you. (: Onne more question, how do you divide radical 50 over radical 49?

Answer 97

\[\frac{\sqrt{50}}{\sqrt{49}} = \frac{\sqrt{50}}{7} = \frac{\sqrt{5\times 5\times 2}}{7} = \frac{5\sqrt{2}}{7}\]