Question

how do you solve
sqrt2(5+sqrt8)^2 ?

A. 66+40 x sqrt2

B. 40+33 x sqrt2

C. 33 x sqrt2

D. 5 x sqrt2 + 4

Answer 1

A. 66+40 x sqrt2

Answer 2

why?

Answer 3

\[\sqrt 2(5 + \sqrt 8)^2\]
right?

Answer 4

i thought it was sqrt(2(5+sqrt(8))^2)

Answer 5

yes @igbasa

Answer 6

uhmm okay..do you know the shortcut to square of a binomial? \[(a+b)^2 = a^2 + 2ab _ b^2\]

Answer 7

\[(a+b)^2 = a^2 + 2ab+ b^2\]

Answer 8

nope :/

Answer 9

uhmm okay we can do it the long way

Answer 10

first let us solve \[(\sqrt 5 + 8)^2\]

Answer 11

And how do we do that?

Answer 12

\[(\sqrt 5 + 8)^2 \implies (\sqrt 5 + 8)(\sqrt 5+ 8)\]
agree?

Answer 13

yess

Answer 14

you're familiar with FOIL right?

Answer 15

very much so

Answer 16

so try foiling that one.

Answer 17

using the radical o.O . Does it still work the same way?

Answer 18

yup..you just have to know a few things
\[\large 1) \; \sqrt a \times \sqrt a = a\]
\[\large 2) \; c \times \sqrt a = c\sqrt a\]

Answer 19

I don't understand why the sqrt of something times the sqrt of itself = a single #?

Answer 20

\[\large \sqrt a \times \sqrt a = \sqrt{a \times a} = \sqrt{a^2} = (a^2)^{1/2} \implies a^{2/2} \implies a^1 \implies a\]

i dont know if you're familiar with the steps i just made...but that's how it's done

Answer 21

I understand it

Answer 22

oh that's nice then

Answer 23

so just do foil and leave the answer within the radical ?

Answer 24

yup

Answer 25

but dont forget..that wont be the final answer yet.. you still have to multiply by \(\sqrt 2\) later on

Answer 26

\[8\sqrt{5} +8\sqrt{5} + \sqrt{25} + 64 ?\]

Answer 27

what's the sqrt of 25?

Answer 28

5

Answer 29

right..so \[8\sqrt 5 + 8\sqrt 5 + 5 + 64\]
you can combine 5 and 64

Answer 30

\[8\sqrt{5} +8\sqrt{5} + 69\]

Answer 31

right.. now think of \(\sqrt 5\) as x..you can combine 8x + 8x right?

Answer 32

yes 16x

Answer 33

so what's \[8 \sqrt 5 + 8\sqrt 5\]

Answer 34

\[8\sqrt{10}?\]

Answer 35

hmm like i said think of \(\sqrt 5\) as x think of \[8 \sqrt 5 + 8\sqrt 5\]
as \[8x + 8x\]

Answer 36

I don't quite understand. Does that mean I would add both numbers by itself twice? or just the number outside of the radical

Answer 37

you add the numbers OUTSIDE the radical..the radical stays the same

Answer 38

\[16\sqrt{5}\]

Answer 39

right so you have \[69 + 16\sqrt 5\]
but this is just \[(\sqrt 5+8)^2\]
you need to multiply by \(\sqrt 2\)

\[\sqrt 2(69 + 16\sqrt 5\]

Answer 40

what you need to sole this is:
\[1) \; a \times \sqrt b = a\sqrt b\]
\[2) \; \sqrt c \times d \sqrt e = d\sqrt{c\times e}\]

Answer 41

so what i assume is that radicalC x D.Radical.E = 16Radical10 ?

Answer 42

right!

Answer 43

:) but what happens to the 69? why wasnt it multiplied by radical 2?

Answer 44

look at number 1 hehe

Answer 45

\[69\sqrt{2}?\]

Answer 46

yup

Answer 47

so what's the final answer

Answer 48

\[69\sqrt{2} + 16\sqrt{10}\]

Answer 49

yup there you go

Answer 50

but that isn't an answer choice O.o

Answer 51

what's the answer coice?

Answer 52

\[A. 66+40\sqrt{2} B. 40+33\sqrt{2} C. 33\sqrt{2} D. 5\sqrt{2}+4\]

Answer 53

WAHHH *facepalm*

Answer 54

we were solving the wrong one T_T you didnt tell me sooner lol

Answer 55

you're joking right?

Answer 56

we were solving \[\sqrt 2(\sqrt 5 + 8)^2\]
we should've solved \[\sqrt 2(5 + \sqrt 8)^2\]
sorry

Answer 57

i totally messed that one up :/

Answer 58

hehe that was funny :3. Hey at least I learned some thing lol :). Maybe this time we can move faster because i have somewhat a clue what i am doing

Answer 59

haha yup

Answer 60

so \[(5 + \sqrt 8)^2 \implies (5 + \sqrt 8)(5+\sqrt 8)\]
now use FOIL

Answer 61

\[5\sqrt{8} + 5\sqrt{8} + 33\]

Answer 62

right. now ad \[5\sqrt 8 + 5\sqrt 8\]

Answer 63

\[10\sqrt{8}\]

Answer 64

right so we have \[\sqrt 2(10 \sqrt 8 + 33)\]

Answer 65

yes. Now I don't know how to distribute that :/

Answer 66

remember \[\sqrt a \times b\sqrt c = b\sqrt{a \times c}\]
\[\sqrt 2 \times 10\sqrt 8 = 10\sqrt{8 \times 2}\]
got it?

Answer 67

lol yup

Answer 68

so what is 8 x 2?

Answer 69

16

Answer 70

and what's the square root of 16?

Answer 71

4

Answer 72

so we have \[\sqrt 2 \times 10 \sqrt 8 \implies 10 \sqrt{8\times 2} \implies 10\sqrt {16} \implies 10 \times 4\] did you get that?

Answer 73

everything up until 10 x 4

Answer 74

\[10 \sqrt {16} \implies 10 \times \sqrt{16} \implies 10 \times 4}\]
now do you get it?

Answer 75

\[10 \sqrt {16} \implies 10 \times \sqrt{16} \implies 10 \times 4\]

Answer 76

*dummy slaps self*

Answer 77

heh lol. so what do you get now?

Answer 78

40 + 33 radical2

Answer 79

:DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD THANK YOU SO MUCH. FOR YOUR PATIENCE AND KINDNESS AND EVERYTHING

Answer 80

hehe <tips imaginary hat> sorry for the constant delayed replies though

Answer 81

:) It's alright. I can't hog your services hehe. Have a really good night(or day depending where you are right now) Igbas :).

Answer 82

hehe you too ^_^