B Question about this Lesson on Square Roots

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The discussion centers on the simplification of square roots, specifically how √27 simplifies to 3√3, which equals approximately 5.196. Confusion arises when trying to relate this to the expression 3²√3, which simplifies to √243 or approximately 15.588. Participants clarify that squaring 3√3 correctly yields 27, while 3²√3 represents a different value. The conversation also includes a brief tutorial on using LaTeX for mathematical notation. Understanding the differences in these expressions is crucial for accurate calculations and simplifications.
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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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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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Likes DaveE and Nugatory
##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.
 
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##.
 
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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