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Mathematics 21 Online
OpenStudy (anonymous):

i need help with math questions

OpenStudy (lilshane):

Everybody does :( But whats your question

OpenStudy (anonymous):

simplify \[3\sqrt{5}-2\sqrt{7}+\sqrt{45}-\sqrt{28}\] please help?

OpenStudy (lilshane):

Is there any answers?

OpenStudy (anonymous):

yes sorry. A. \[2\sqrt{12}\] B. \[2\sqrt{2}\] C. \[6\sqrt{5}-4\sqrt{7}\] D. \[6\sqrt{10}-4\sqrt{14}\]

OpenStudy (lilshane):

@iGreen Can you help with this??

OpenStudy (igreen):

Okay, we have to simplify the square root of 45 and the square root of 28. @rikkibracamonte1999

OpenStudy (anonymous):

Okay :)

OpenStudy (igreen):

Okay, find the factors of 45 and 28..can you do that?

OpenStudy (anonymous):

yes i can

OpenStudy (igreen):

Okay, tell me what you get.

OpenStudy (anonymous):

Factors of 45: 1,3,5,9,15 and 45 Factors of 28: 1,2,4,7,14 and 28

OpenStudy (igreen):

Nice work, now which of those are perfect squares?

OpenStudy (igreen):

Do you know what a perfect square is?

OpenStudy (anonymous):

no i do not

OpenStudy (anonymous):

can you possibly explain it to me?

OpenStudy (igreen):

Okay, perfect squares are numbers that we can get by multiplying two whole numbers together. 81 is a perfect square because the square root of 81 is 9, which is a whole number. 121 is also a perfect square because the square root of 121 is 11, which is also a whole number.

OpenStudy (igreen):

Factors of 45: 1,3,5,9,15 and 45 Factors of 28: 1,2,4,7,14 and 28 So which of those numbers up there are perfect squares?

OpenStudy (anonymous):

For 45 i am gonna say 1 and 45 For 28 i am gonna say 2 and 14

OpenStudy (igreen):

No, if you plug them into your calculator to find the square root, you get decimals..so they're incorrect.

OpenStudy (anonymous):

sorry :)

OpenStudy (anonymous):

i meant :(

OpenStudy (anonymous):

math is not my best subject

OpenStudy (igreen):

Okay, 9 and 4 are the perfect squares. 9 because the square root of 9 is 3, and 4 because the square root of 4 is 2.

OpenStudy (igreen):

So we can break up the square root of 45 into: \(\sf \sqrt{9} \times \sqrt{5}\)

OpenStudy (anonymous):

Okay :)

OpenStudy (igreen):

And the square root of 9 is what?

OpenStudy (anonymous):

3

OpenStudy (igreen):

Yes, so we have: \(\sf 3 \times \sqrt{5}\) or \(\sf 3\sqrt{5}\)

OpenStudy (igreen):

We can break up the square root of 28 into: \(\sf\sqrt{4} \times \sqrt{7}\) What's the square root of 4?

OpenStudy (anonymous):

2

OpenStudy (igreen):

Yes, so we have: \(\sf 2 \times \sqrt{7}\) or \(\sf 2\sqrt{7}\)

OpenStudy (igreen):

So we have: \(\sf 3\sqrt{5}-2\sqrt{7}+3\sqrt{5}-2\sqrt{7}\) Combine the like terms. \(\sf 3\sqrt 5 + 3 \sqrt 5 =~ \! ?\) \(\sf -2 \sqrt{7} - 2\sqrt 7\) Just add 3 + 3 and subtract -2 - 2 and keep the square roots.

OpenStudy (anonymous):

so............ its b?

OpenStudy (anonymous):

because i did what you said to do

OpenStudy (igreen):

You got it! \(\sf 3 \sqrt 5 + 3 \sqrt 5 = 6 \sqrt 5\) \(\sf -2 \sqrt 7 – 2 \sqrt 7 = -4 \sqrt 7\) So we have: \(\sf 6 \sqrt 5 – 4 \sqrt 7\)

OpenStudy (igreen):

\(\color{lime}{\underbrace{\overbrace{\Huge\bigstar\star\ast\bigstar\star\ast\bigstar\star\ast\bigstar\star\ast\\\bigstar\star\ast\bigstar\star\ast\bigstar\star\ast\bigstar\star\ast\bigstar\star\ast\bigstar\star\ast\bigstar\star\ast\bigstar\star\ast\bigstar\star\ast\bigstar\star\ast\\\Large{~\succ}\bigstar\boxed{\sf Welcome~to~\color{#3dabea}{Open}\color{#9cc575}{Study}!!!}\bigstar\hspace-5px\prec\\\bigstar\star\ast\bigstar\star\ast\bigstar\star\ast\bigstar\star\ast\bigstar\star\ast\bigstar\star\ast\bigstar\star\ast\bigstar\star\ast\bigstar\star\ast\bigstar\star\ast\\\Huge{\bigstar\star\ast\bigstar\star\ast\bigstar\star\ast\bigstar\star\ast}}}}\) \(\small\sf\color{red}{Made~by~@nobrainiachere,~edited~by~@iGreen}\) You can give medals by clicking 'Best Response'.

OpenStudy (anonymous):

how about this? Is the simplified form of \[2\sqrt{3}\times2\sqrt{6}\] rational? A. Yes B. No

OpenStudy (anonymous):

please help @iGreen . Your the best with these types of questions

OpenStudy (anonymous):

@texaschic101 @iGreen @bohotness plz help?

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