Disgruntledstudent Disgruntledstudent
  • 02-05-2019
  • Mathematics
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How to simplify the square root of 3 over the square root of 21

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LammettHash
LammettHash LammettHash
  • 02-05-2019

3 * 7 = 21, so

[tex]\sqrt{21}=\sqrt{3\cdot7}=\sqrt3\sqrt7[/tex]

Then

[tex]\dfrac{\sqrt3}{\sqrt{21}}=\dfrac1{\sqrt7}[/tex]

and you can rationalize the denominator to write this as

[tex]\dfrac1{\sqrt7}\cdot\dfrac{\sqrt7}{\sqrt7}=\dfrac{\sqrt7}7[/tex]

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angie823
angie823 angie823
  • 02-05-2019

answer: √3⋅√21 = 3√7

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