High School Question about this Lesson on Square Roots

[Simon Peach]

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?

 

[andrewkirk]

if I say 3squard (root)3

Why would you say that? It ($3^2\sqrt 3$) has nothing to do with $\sqrt {27}=3\sqrt 3=5.196...$.

 

[Mark44]

$3^2\sqrt 3= \sqrt{9^2 \cdot 3} = \sqrt{243}$
$3\sqrt3 = \sqrt{9 \cdot 3} = \sqrt{27}$
It should be obvious that we're talking about different numbers.

 

[PeterDonis]

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 $3^2 \times 3 = 9 \times 3 = 27$.

 

[Mark44]

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.