Respuesta :

itzshiane

Answer:

[See Below]

Step-by-step explanation:

[tex]\boxed{Hey~There!}[/tex]

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[tex]\boxed{Simplify~each~radical:}[/tex]

1.) [tex]\sqrt{72}[/tex]:

  • Factor [tex]72[/tex] into its prime factors :

          [tex]72 = 23 * 32[/tex]  

  • 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:

          [tex]36 = 22 * 32[/tex]  

  • Factors which will remain inside the root are:

          [tex]2 = 2[/tex]  

  • 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 [tex]2[/tex]:

          [tex]6 = 2 * 3[/tex]

[tex]\boxed{The~answer~is: 6\sqrt{2}}[/tex]

2.) [tex]\sqrt{20}[/tex]:

  • Factor [tex]20[/tex] into its prime factors :

          [tex]20 = 22 * 5[/tex]  

  • 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:

         [tex]4 = 22[/tex]

  • Factors which will remain inside the root are:

          [tex]5 = 5[/tex]  

  • 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 [tex]2[/tex]:

          [tex]2 = 2[/tex]

[tex]\boxed{The~answer~is: 2\sqrt{5}}[/tex]

3.) [tex]\sqrt{42}[/tex]:

  • Factor [tex]42[/tex] into its prime factors :

          [tex]42 = 2 * 3 * 7[/tex]

  • 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 .

[tex]\boxed{The~answer~is: \sqrt{42} }[/tex]

4.) [tex]2\sqrt{12}[/tex]:

  • Factor [tex]12[/tex] into its prime factors :

          [tex]12 = 22 * 3[/tex]  

  • 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:

          [tex]4 = 22[/tex]  

  • Factors which will remain inside the root are:

          [tex]3 = 3[/tex]  

  • 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 [tex]2[/tex]:

          [tex]2 = 2[/tex]

[tex]\boxed{The~answer~is: 4\sqrt{3} }[/tex]

5.) [tex]3\sqrt{75}[/tex]:

  • Factor [tex]75[/tex] into its prime factors :

          [tex]75 = 3 * 52[/tex]  

  • 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:

          [tex]25 = 52[/tex]  

  • Factors which will remain inside the root are:

          [tex]3 = 3[/tex]  

  • 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 [tex]2[/tex]:

          [tex]5 = 5[/tex]

[tex]\boxed{The~answer~is: 15\sqrt{3}}[/tex]

6.) [tex]-2\sqrt{18}[/tex]:

  • Factor [tex]18[/tex] into its prime factors :

          [tex]18 = 2 * 32[/tex]  

  • 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:

         [tex]9 = 32[/tex]  

  • Factors which will remain inside the root are:

          [tex]2 = 2[/tex]  

  • 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 [tex]2[/tex]:

          [tex]3 = 3[/tex]

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

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[tex]Hope~this~helps~Mate~\\-Your~Friendly~Answerer,~Shane[/tex]  ^-^