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ella [17]
3 years ago
11

Simplify each radical And show your work √72 √20 √42 2√12 3√75 -2√18​

Mathematics
1 answer:
Bogdan [553]3 years ago
8 0

Answer:

[See Below]

Step-by-step explanation:

\boxed{Hey~There!}

__________________________________________________________

\boxed{Simplify~each~radical:}

1.) \sqrt{72}:

  • Factor 72 into its prime factors :

          72 = 23 * 32  

  • To simplify a square root, we extract factors which are squares, factors that are raised to an even exponent.
  • Factors which will be extracted are:

          36 = 22 * 32  

  • Factors which will remain inside the root are:

          2 = 2  

  • To complete the simplification we take the square root of the factors which are to be extracted. We do this by dividing their exponents by 2:

          6 = 2 * 3

\boxed{The~answer~is: 6\sqrt{2}}

2.) \sqrt{20}:

  • Factor 20 into its prime factors :

          20 = 22 * 5  

  • To simplify a square root, we extract factors which are squares, factors that are raised to an even exponent.
  • Factors which will be extracted are:

         4 = 22

  • Factors which will remain inside the root are:

          5 = 5  

  • To complete the simplification we take the square root of the factors which are to be extracted. We do this by dividing their exponents by 2:

          2 = 2

\boxed{The~answer~is: 2\sqrt{5}}

3.) \sqrt{42}:

  • Factor 42 into its prime factors :

          42 = 2 * 3 * 7

  • To simplify a square root, we extract factors which are squares, factors that are raised to an even exponent.
  • In our case however, all the factors are only raised to the first power and this means that the square root can not be simplified .

\boxed{The~answer~is: \sqrt{42} }

4.) 2\sqrt{12}:

  • Factor 12 into its prime factors :

          12 = 22 * 3  

  • To simplify a square root, we extract factors which are squares, factors that are raised to an even exponent.
  • Factors which will be extracted are:

          4 = 22  

  • Factors which will remain inside the root are:

          3 = 3  

  • To complete the simplification we take the square root of the factors which are to be extracted. We do this by dividing their exponents by 2:

          2 = 2

\boxed{The~answer~is: 4\sqrt{3} }

5.) 3\sqrt{75}:

  • Factor 75 into its prime factors :

          75 = 3 * 52  

  • To simplify a square root, we extract factors which are squares, factors that are raised to an even exponent.
  • Factors which will be extracted are:

          25 = 52  

  • Factors which will remain inside the root are:

          3 = 3  

  • To complete the simplification we take the square root of the factors which are to be extracted. We do this by dividing their exponents by 2:

          5 = 5

\boxed{The~answer~is: 15\sqrt{3}}

6.) -2\sqrt{18}:

  • Factor 18 into its prime factors :

          18 = 2 * 32  

  • To simplify a square root, we extract factors which are squares, factors that are raised to an even exponent.
  • Factors which will be extracted are:

         9 = 32  

  • Factors which will remain inside the root are:

          2 = 2  

  • To complete the simplification we take the square root of the factors which are to be extracted. We do this by dividing their exponents by 2:

          3 = 3

\boxed{The~answer~is: 3\sqrt{5}~or~-6\sqrt{2}}

__________________________________________________________

Hope~this~helps~Mate~\\-Your~Friendly~Answerer,~Shane  ^-^

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Hey there,
Let's say that the first piece is x cm
1st = x
2nd = x + 25%
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100% = 240 cm
1% = 240 / 100
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x + x + 25 + x - 25 = 100
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x = 240 / 3
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Hope this helps :))

<em>~Top♥</em>
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Step-by-step explanation:

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Sally has 600 ml of drink
Karen has 600 ml of lime juice

When it is mixed at a ratio of 2:7:3 . . .pineapple:orange:lime (respectively) . . this means . . . there are a total of 2 + 7 + 3 parts = 12 parts . . and each part individually is as follows:

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Sally has 12 parts = 600 ml of drink
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 . . orange = 7/12*600ml = 350 ml orange
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We know Karen has 600 ml of lime juice and if that is 3/12 of the total, then 600*12/3 = the total drink = 2400 ml of drink

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Thus . . . (for Karen) . . .
<u><em>A = 2400 ml of drink</em></u>
<u><em>B = 400 ml of orange juice</em></u>
<u><em>C = 1400 ml of pineapple juice</em></u>




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