Anguyennn
  • Anguyennn
how to simplify 2√4-√9?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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jim_thompson5910
  • jim_thompson5910
What is the square root of 4 equal to?
Anguyennn
  • Anguyennn
2
jim_thompson5910
  • jim_thompson5910
correct What is the square root of 9 equal to?

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More answers

Anguyennn
  • Anguyennn
3
Anguyennn
  • Anguyennn
and you multiply 2x2 and minus 3? correct?
jim_thompson5910
  • jim_thompson5910
so you really have `2*2-3` evaluate that to get ??
jim_thompson5910
  • jim_thompson5910
correct
Anguyennn
  • Anguyennn
oh ok!! thank you but what about when its √2?
jim_thompson5910
  • jim_thompson5910
taking the square root of 2 doesn't give a whole number like the square root of 4 does
Anguyennn
  • Anguyennn
like 3√2-5√2-2√2
jim_thompson5910
  • jim_thompson5910
I don't see a square root of 2 in your problem though
jim_thompson5910
  • jim_thompson5910
Oh I see now
jim_thompson5910
  • jim_thompson5910
replace every copy of "square root of 2" with x so you'll have 3x-5x-2x simplify that to get ???
Anguyennn
  • Anguyennn
-4x
Anguyennn
  • Anguyennn
but how come you replaced it with an x?
jim_thompson5910
  • jim_thompson5910
well you don't need to, but you can think of it like that basically you're combining like terms. In this case, all 3 terms are like terms because they have a root 2 in them
Anguyennn
  • Anguyennn
yes
jim_thompson5910
  • jim_thompson5910
3x-5x-2x = -4x so you now replace the x with square root of 2 so the final answer is \(\Large -4\sqrt{2}\)
Anguyennn
  • Anguyennn
i am still confused because for other questions it would have different numbers and i don't know how to do them
jim_thompson5910
  • jim_thompson5910
like what for example?
Anguyennn
  • Anguyennn
√18+√50-√8
jim_thompson5910
  • jim_thompson5910
have you tried to simplify each root?
Anguyennn
  • Anguyennn
dividing them all by 2?
jim_thompson5910
  • jim_thompson5910
think of all of the factors of 18 which factors are perfect squares?
Anguyennn
  • Anguyennn
I am not sure
Anguyennn
  • Anguyennn
sorry
jim_thompson5910
  • jim_thompson5910
factors of 18 1,2,3,6,9,18
Anguyennn
  • Anguyennn
ok
jim_thompson5910
  • jim_thompson5910
which factor is a perfect square?
Anguyennn
  • Anguyennn
9
jim_thompson5910
  • jim_thompson5910
so we can say this \[\Large \sqrt{18} = \sqrt{9*2}\] \[\Large \sqrt{18} = \sqrt{9}*\sqrt{2}\] \[\Large \sqrt{18} = 3*\sqrt{2}\]
jim_thompson5910
  • jim_thompson5910
I factored 18 into 9*2 then I used the rule \[\Large \sqrt{x*y} = \sqrt{x}*\sqrt{y}\]
Anguyennn
  • Anguyennn
yes
jim_thompson5910
  • jim_thompson5910
now let's do 50 what are the factors of 50?
Anguyennn
  • Anguyennn
1, 2, 5, 10, 25
Anguyennn
  • Anguyennn
and it would be 25 that is the perfect square
jim_thompson5910
  • jim_thompson5910
yes so 50 = 25*2
jim_thompson5910
  • jim_thompson5910
what would \(\Large \sqrt{50}\) simplify to?
Anguyennn
  • Anguyennn
√25x2
jim_thompson5910
  • jim_thompson5910
then break it up using the rule I posted
Anguyennn
  • Anguyennn
√50= √25x2 =√25x √2 5√2
jim_thompson5910
  • jim_thompson5910
good
jim_thompson5910
  • jim_thompson5910
now onto 8 the factors of 8 are ???
Anguyennn
  • Anguyennn
1,2,4,8
jim_thompson5910
  • jim_thompson5910
which is a perfect square?
Anguyennn
  • Anguyennn
√4
jim_thompson5910
  • jim_thompson5910
so we can say 8 = 4*2
jim_thompson5910
  • jim_thompson5910
then use that rule
Anguyennn
  • Anguyennn
√8= √4x2 =√4x√2 2√2
jim_thompson5910
  • jim_thompson5910
so, \[\Large \sqrt{18}+\sqrt{50}-\sqrt{8}\] is the same as \[\Large 3\sqrt{2}+5\sqrt{2}-2\sqrt{2}\]
jim_thompson5910
  • jim_thompson5910
we can replace all the square root of 2 terms with x \[\Large 3\color{red}{\sqrt{2}}+5\color{red}{\sqrt{2}}-2\color{red}{\sqrt{2}}\] \[\Large 3\color{red}{x}+5\color{red}{x}-2\color{red}{x}\]
Anguyennn
  • Anguyennn
correct
Anguyennn
  • Anguyennn
is that the answer?
jim_thompson5910
  • jim_thompson5910
not yet
Anguyennn
  • Anguyennn
would you do 3+5-2 now?
Anguyennn
  • Anguyennn
and get 6√2?
jim_thompson5910
  • jim_thompson5910
very good, that's your final answer
Anguyennn
  • Anguyennn
oh ok thank you so much!
jim_thompson5910
  • jim_thompson5910
you're welcome

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