anonymous
  • anonymous
what is the value of the expression sqrt(27)+sqrt(32)-sqrt(75)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\sqrt(27)+\sqrt(32)-\sqrt(75)\]
anonymous
  • anonymous
@zaynahf if your not busy can you help me out?
anonymous
  • anonymous
Sure, i can! Do you know how to simplify radicals?

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anonymous
  • anonymous
not really
anonymous
  • anonymous
>< ---
anonymous
  • anonymous
To simplify radicals, you have to try to find a perfect square that fits perfectly into the number. So for the first one: \[\sqrt{27}\] the biggest perfect square that can fit into it is 9. So, the inside would simplify to be: \[\sqrt{9 \times 3} = 3\sqrt{3}\]
anonymous
  • anonymous
so i can get \[\sqrt16X2 = 4\sqrt2 ?\]
anonymous
  • anonymous
Yeah! Now try the third one
anonymous
  • anonymous
\[\sqrt75 = \sqrt5X15 = 5\sqrt5?\]
anonymous
  • anonymous
No, since neither 15 nor 5 are perfect squares. Here are the perfect squares: 1,4,9,16,25,36,49,64,81,100....
anonymous
  • anonymous
so \[aaaannnnnd`im lost\]
anonymous
  • anonymous
lol i'll guide you through
anonymous
  • anonymous
ok
anonymous
  • anonymous
Ok since you want to get the biggest one that goes into there, start from the top of the list. Try seeing if 100 goes into 75 (obviously not), so just start from the smallest number after 75. 64,36,25,16,4,1. When you find the one that goes into 72, let me know.
anonymous
  • anonymous
64
anonymous
  • anonymous
64 goes into 75 evenly?
anonymous
  • anonymous
oh no 25
anonymous
  • anonymous
Good! Now what times 25 is 75?
anonymous
  • anonymous
3
anonymous
  • anonymous
So thats what goes under the radical: \[\sqrt{75}= \sqrt{25 \times 3}= 5\sqrt{3}\] Right?
anonymous
  • anonymous
ok what do i do now multiply them together?
anonymous
  • anonymous
\[3\sqrt{3}+4\sqrt{2}-5\sqrt{3}\] Is that what you have so far?
anonymous
  • anonymous
yes
anonymous
  • anonymous
There are only 2 with the same base radical, so you can only simplify those
anonymous
  • anonymous
so i get \[8\sqrt3+ 4\sqrt2\]
anonymous
  • anonymous
Remember, it's 3-5, not 3+5
anonymous
  • anonymous
-2√3+4√2
anonymous
  • anonymous
is that my final answer?
anonymous
  • anonymous
Perfect
anonymous
  • anonymous
Yes it is
anonymous
  • anonymous
thnxs so much ^_^ now i can sleep ... eh maybe
anonymous
  • anonymous
No problem! Let me know if you need other help

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