Question about this Lesson on Square Roots

You can also find links to this and other tutorials in our Information subreddit, which is always one click away from any page you're on.In summary, the conversation discusses the simplification of ##\sqrt{27}## and ##3\sqrt{3}##. It is important to square all terms when trying to find the square of a square root.
  • #1
Simon Peach
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In a lesson on square roots this came up (Root) 27 simplifies too 3(root)3 ok. when I work that out it's
= 5.196... or if I say 3squard (root)3 this works out to 15.588.... What am I missing?
 
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  • #2
Simon Peach said:
if I say 3squard (root)3
Why would you say that? It (##3^2\sqrt 3##) has nothing to do with ##\sqrt {27}=3\sqrt 3=5.196...##.
 
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  • #3
##3^2\sqrt 3= \sqrt{9^2 \cdot 3} = \sqrt{243}##
##3\sqrt3 = \sqrt{9 \cdot 3} = \sqrt{27}##
It should be obvious that we're talking about different numbers.
 
  • #4
Simon Peach said:
if I say 3squard (root)3
If you're trying to square ##3 \sqrt{3}## to see if it comes out to 27, you need to square everything: you get ##3^2 \times 3 = 9 \times 3 = 27##.
 
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  • #5
Simon Peach said:
In a lesson on square roots this came up (Root) 27 simplifies too 3(root)3 ok. when I work that out it's
= 5.196... or if I say 3squard (root)3 this works out to 15.588.... What am I missing?
@Simon Peach, you're a little older than I am, but not by very much. Here's a quick lesson on some of the features of LaTeX that are supported on this site:

Your notation.........Rendered LaTeX...............Raw LaTeX
(Root) 27 .........................##\sqrt{27}##..............................##\sqrt{27}##
3(root)3 ...........................##3\sqrt 3##..............................##3\sqrt 3##
3squard (root)3..............##3^2\sqrt 3##...........................##3^2\sqrt 3##

The link in the lower left corner of the input pane goes to our LaTeX tutorial.
 

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