Question

help please!
what is the simplest form of the expression ?

Answer 1

\[\sqrt[3]{45}+\sqrt[3]{2058}-\sqrt[3]{750}\]

Answer 2

Find prime factors of each of the numbers within the cube root:

45 = 3 x 3 x 5
2058 = 2 x 3 x 7 x 7 x 7
750 = 2 x 3 x 5 x 5 x 5

Take the cube root of each and evaluate the expression and simplify.

Answer 3

\[\sqrt[3]{9}.\sqrt[3]{5} + \sqrt[3]{343}.\sqrt[3]{6} - \sqrt[3]{125}.\sqrt[3]{6}\]\[\sqrt[3]{9} . \sqrt[3]{5} + 7 . \sqrt[3]{6} - 5 . \sqrt[3]{6}\]\[\sqrt[3]{9} . \sqrt[3]{5} + 2\sqrt[3]{6}\]

Answer 4

can you explain how you got that?

Answer 5

so wat i did was that i took the 45 and broke it up into 9 and 5, then i took 2058 and broke it up into 343 and 6, then i took 750 and broke it up into 125 and 6

Answer 6

because 9x5 = 45
343x6=2058
and 125 x 6 = 750
cool?

Answer 7

yeah i got it. thanks you

Answer 8

ok and u understand everything i did after that?

Answer 9

nope can you explain that too

Answer 10

ofc!

Answer 11

next the cude root of 343 is 7 and the cude root of 125 is 5

Answer 12

and then after that 7 times the cude root of 6 minus by 5 times the cude root of 6 = 2 times the cube root of 6

Answer 13

thank you! can you help me on a few more questions i got wrong

Answer 14

yea np :)

Answer 15

\[\sqrt[3]{108}+\sqrt[3]{1372}-\sqrt[3]{500}\]

Answer 16

would u rather we do it together or u prefer that i do it and then explain?

Answer 17

together

Answer 18

ok so look at the 3 cude roots and see if there is a number that u can break it up into so that u can find the cude root of it
example\[\sqrt[3]{750}=\sqrt[3]{125}\sqrt[3]{6}=5\sqrt[3]{6}\]

Answer 19

in this case i broke 750 into 125 and 6 cause i knew the cude root of 125 is 5

Answer 20

okay then what

Answer 21

well i want u to tell me if any of them could be splitted up to do that

Answer 22

a hint is that\[\sqrt[3]{500}\]could be broken up into two numbers and one of them u can find the square root of, try and tell me wat aare those two numbers

Answer 23

7.937?

Answer 24

im sry but i have to go :/ ill be back in 30mins, hopfully u'll still be here

Answer 25

i will

Answer 26

back

Answer 27

okay

Answer 28

do you know how to do surds?

Answer 29

whats that

Answer 30

basically wat u have to know to do this question

Answer 31

like
Let C = A x B
therefore
\[\sqrt{C} = \sqrt{A}\sqrt{B}\]

Answer 32

i have no idea

Answer 33

ok well this is something u have to just accept
Learn that if two numbers are being multiplied and they are square rooted
example \[\sqrt{2 x 3}\]
that is equal to the square root of them separatly, example
\[\sqrt{2}\sqrt{3}\]
Therefore
\[\sqrt{2 x 3} =\sqrt{2}\sqrt{3}\]

Answer 34

understand?

Answer 35

yes

Answer 36

cool so how you are going to use this is that if u are told to simplify the following \[\sqrt{50}\]
then you'll use surds to do this
\[\sqrt{25x2}\]\[\sqrt{25}\sqrt{2}\]\[5\sqrt{2}\]
cool?

Answer 37

yes

Answer 38

so back to ur question\[\sqrt[3]{108}+\sqrt[3]{1372}-\sqrt[3]{500}\]

Answer 39

now i want u to simplify \[\sqrt[3]{500} \] using that method

Answer 40

how's it going?