Question

how do i figure out what's the hypotenuse of a right triangle when the base and height have a sq. root along side the number?

Answer 1

Do you have the specific numbers?

Answer 2

the base and height is 5 sq. rooted

Answer 3

hypotenuse^2=base^2+height^2

Answer 4

that's what i was thinking unkle but how would i go about doing it?
im not too math smart, sorry.

Answer 5

Well, do you happen to know what exponent is the same as a square root?

Answer 6

elaborate, please.

Answer 7

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

Answer 8

so, i would set up the problem like so...\[5\frac{ 1 }{ 2 }^{2} + 5\frac{ 1 }{ 2 }^{2} = c ^{2} ??\]

Answer 9

im trying to figure it out. im sorry.

Answer 10

A square root is the same as a 1/2 power. So when you need to square this, it looks like this:
\[(5^{\frac{ 1 }{ 2 }})^{2}\]
When you have an exponent that is being raised to another exponent, in this case an exponent of (1/2) that is being squared, you just multiply the exponents. So what is (1/2)*2?

Answer 11

\[(5^{1/2})^2=5^{2/2}=\]

Answer 12

oooo.. i think im starting to get it.
let me do this on paper, and ill post back my answer in a few seconds

Answer 13

Sure :3

Answer 14

c would equal 10 ?

Answer 15

not quite

Answer 16

i thought so

Answer 17

didn't look right on paper.

Answer 18

You would have this:
\[\sqrt{5^{\frac{ 1 }{ 2 }*2}+5^{\frac{ 1 }{ 2 }*2}}=\sqrt{5^{1}+5^{1}} \]

Answer 19

would it then be 10 sq. ?

Answer 20

Correct :3

Answer 21

YYYEEESSSSSSSS

Answer 22

yes, the hypo is √10 \(\checkmark\)

Answer 23

thank you psymon and unkle ruck, what do i do now after i get help, do i hit the best response thingy?

Answer 24

Its not necessary xD It just gives one of us some medal thingy.

Answer 25

yes, hit best response if you want, then close the question, and then you will be able to open a new questioin

Answer 26

aww man, alrighty. i still wanna thank you guys. im doing this quiz that ive been stuck on for a while because i was too afraid of failing again.

Answer 27

Well we always got people around to try and help :3

Answer 28

\[\color{orange}{\ddot\smile}\]

Answer 29

awww man, the quiz told me it was wrong

Answer 30

it* said it was 10 not 10 sq.

Answer 31

what?

Answer 32

idk.

Answer 33

a^2 + b^2 = c^2
a = sqrt(5) b = sqrt(5)
therefore
\[\sqrt{5}^{2}+\sqrt{5}^{2}=c ^{2} \]
\[10=c ^{2}->c=\sqrt{10}\]

Answer 34

let me do this on paper. uno momento

Answer 35

forgive me, laptop is slow, im typing out the equation

Answer 36

as you have worded the question above the hypotenuse is √10 as we have found.
was the question in the quiz worded slightly differently ?

Answer 37

\[5\sqrt{2}^{2} + 5\sqrt{2}^{2} = c ^{2}\]

Answer 38

Now thats 100% different.

Answer 39

oh right, do you mean
?
\[(5\sqrt{2})^{2} + (5\sqrt{2})^{2} = c ^{2}\]

Answer 40

In that case it would be 10.

Answer 41

i typed it before only with sq. root as 1/2 fraction, where was the error?

Answer 42

Its a 1/2 exponent. Just like squared is an exponent of 2, square root is an exponent of 1/2.

Answer 43

alright, seeing that's the case, can you do the equation so i can see how it would be set up ?

Answer 44

i learn from example

Answer 45

Well, the reason i wrote it as a 1/2 exponent was to help show you how you actually square it. But this is how I would go about it. Now remember, a square root is a 1/2exponent and if you square a square root, it just makes the square root go away. So this is how I'd write it:

\[(5\sqrt{2})^{2}+(5\sqrt{2})^{2}=c ^{2}\]Now the key here is knowing I can rewrite the problem like this:
\[5^{2}\sqrt{2}^{2}+5^{2}\sqrt{2}^{2}=c ^{2}\]You have to be aware that we are squaring everything. The 5 is squared as well as the sqrt(2). So this becomes:
\[5^{2}2^{\frac{ 1 }{ 2 }*2}+5^{2}2^{\frac{ 1 }{ 2 }*2}\]
\[(25)(2)^{1}+(25)(2)^{1}=c ^{2}\]
\[50+50=c ^{2}->100=c ^{2}->\sqrt{100}=c->c=10\]

Answer 46

the part where the 2 has the fraction and the exponent, can you explain to me how does that happen?

Answer 47

Right. Well remember
\[\sqrt{x}=x ^{\frac{ 1 }{ 2 }}\]
The reason I write it like that is because then you can see that you have a 1/2 exponent being multiplied by a 2 exponent. Let's say I had this:
\[(\sqrt{x})^{4} \]
Well now we have a 4 power. It may not be obvious how to do that, but if we know that
\[\sqrt{x}=x ^{\frac{ 1 }{ 2 }} \]then we can make more sense of this example. What we have is:
\[x ^{\frac{ 1 }{ 2 }*4}=x ^{2} \]So the reason I put it as a 1/2 exponent is just to visually show you how we go about squaring, taking the 4th power, or doing anything to a square root.

Answer 48

the symbol becomes the fraction?

Answer 49

Right. They are the same thing.
\[\sqrt{x}=x ^{\frac{ 1 }{ 2 }}\]A square root is just like having a 1/2 up there. Same thing. I just rewrote it as the fraction because it makes it easier to see what happens when you square it because it just becomes 1/2 * 2

Answer 50

sorry ive been prolonging the convo, i just like multiple types clarification on things i dont grasp too quickly. now to be sure, can you give me an example problem?

Answer 51

You want to invent something maybe?

Answer 52

literal or you mean something else?

Answer 53

Like invent a problem that you think might be good to have explained to you. So I can show you how I would handle all thwe square roots and powers.

Answer 54

\[3\sqrt{5}^{2} + 7\sqrt{11}^{2} = c ^{2}\]

Answer 55

You mean for the 3 and the 7 to be squared, too, right?

Answer 56

I think you do, so Ill show ya.

Answer 57

i hope my answer is the same as yours.

Answer 58

\[(3\sqrt{5})^{2}+(7\sqrt{11})^{2}\]
So again, I want to make sure I square everything. That means I need to square the 3 and the sqrt(5) in the first problem. Square the 7 as well as the sqrt(11) in the 2nd one. So since I want to square everything, I can rewrite it like this:
\[(3)^{2}(\sqrt{5})^{2}+(7)^{2}(\sqrt{11})^{2}=c ^{2}\]Now this is just so you can visually see what Im doing. Again, those square roots are just like having a 1/2 up there right next to the 2 power. So I'll rewrite it like that.
\[(3)^{2}(5)^{\frac{ 1 }{ 2 }*2}+(7)^{2}(11)^{\frac{ 1 }{ 2 }*2}=c ^{2}\]Now having that 1/2 and that 2 up there, they get multiplied and just become 1. So now I have:
\[(3)^{2}(5)+(7)^{2}(11)=c ^{2}\]
3 squared is 9 and 7 squared is 49, so I can fill those in:
\[(9)(5)+(49)(11)=c ^{2}\]
\[45+539=c ^{2}\]
\[588=c ^{2}\]
\[c=\sqrt{588}\]
So that would be your answer. Have they shown you how to simplify radical expressions?

Answer 59

it's 584 actually lol

Answer 60

584 aq. rooted

Answer 61

Yeah, my bad, I didnt even look xD I just was typing as I was going xD

Answer 62

lol, so i got it right this time

Answer 63

Awesome :D

Answer 64

alright, thank you. im gonna try to finish my quiz now, thank you. i might come back for more mathematical wisdom soon.

Answer 65

Yeah, np. We'll be glad to help :3