Solving Evaluate 3 * sqr(2): Understanding the Method

  • Context: MHB 
  • Thread starter Thread starter Ziggletooth
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around evaluating the expression 3 * sqrt(2) and understanding the method used to manipulate square roots in mathematical expressions. Participants explore the implications of squaring factors and the conditions under which certain manipulations are valid, while also addressing confusion arising from comparing different expressions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about evaluating 3 * sqrt(2) and suggests squaring both factors to eliminate the square root, leading to the incorrect conclusion that it equals 18.
  • Another participant points out that the manipulation of 2 * sqrt(16) to arrive at 64 is incorrect, emphasizing that 2 * sqrt(16) should equal 8.
  • A third participant suggests that the confusion may stem from misunderstanding how to properly manipulate square roots and proposes that 3 * sqrt(2) can be rewritten as sqrt(9 * 2) = sqrt(18).
  • There is a discussion about the validity of "throwing away" the square root and the importance of recognizing the context in which these operations are performed.
  • A later reply clarifies that the original intent was to compare two expressions rather than evaluate them, which contributed to the misunderstanding.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the method of manipulation for square roots, as there are differing views on how to approach the evaluation and comparison of the expressions involved. The discussion remains unresolved regarding the best method to handle such evaluations.

Contextual Notes

Participants highlight limitations in their understanding of the operations involving square roots, particularly in terms of context and the assumptions underlying their manipulations.

Ziggletooth
Messages
5
Reaction score
0
I'm having trouble understanding how this method works and why it appears not to work on similar questions.

For the question evaluate 3 * sqr(2)

I understand I can square both factors to eliminate the square root.

(3 * 3) * 2 = 18

However this does not appear to work with 2 * sqr(16)

(2 * 2 ) * 16 = 64

But the answer is 2 * 4 = 8. I can see why that is, because 4 is the sqr(16), but I don't understand why the previous method failed on what appears to me to be essentially the same question.

Any help would be appreciated, thank you.
 
Mathematics news on Phys.org
You correctly stated that $$2 \sqrt{16} \neq 64$$.

Why would you believe that $$3 \sqrt{2}=18$$? These two are not equal in the same way that the first two are not equal.
 
Ziggletooth said:
I'm having trouble understanding how this method works and why it appears not to work on similar questions.

For the question evaluate 3 * sqr(2)

I understand I can square both factors to eliminate the square root.

(3 * 3) * 2 = 18
Yes, you can but how does that help you evaluate [math]3\sqrt{2}[/math]?

I suspect that you are thinking, instead, of "taking the '3' inside the square root":
[math]3\sqrt{2}= \sqrt{9(2)}= \sqrt{18}[/math].

However this does not appear to work with 2 * sqr(16)

(2 * 2 ) * 16 = 64
But it does work: [math]2\sqrt{16}= \sqrt{4(16)}=\sqrt{64}[/math]

But the answer is 2 * 4 = 8. I can see why that is, because 4 is the sqr(16), but I don't understand why the previous method failed on what appears to me to be essentially the same question.

Any help would be appreciated, thank you.
You can't just "throw away" the square root. If the problem is to find a\sqrt{b} then you can "take the a inside the square root" to get [math]\sqrt{a^2b}[/math] but you still have to take the square root!

Actually most people would consider "simplifying" a square root to be going the other way: to simplify [math]\sqrt{18}[/math] write it as [math]\sqrt{9(2)}= 3\sqrt{2}[/math].
 
I'm sorry it appears the source of my confusion was very much that I assumed I was evaluating something when in fact I was originally doing these operations to make it easier to compare which of two expressions were greater. That wasn't clear to me at the time so I was confused why it wasn't working is some cases but it depended on the context of the numbers I was comparing.

Thanks
 

Similar threads

MHB Why Can't a Right Triangle Have Sides that Add Up to the Area of Squares?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Is the Calculation of $(3 \diamond 8) \square 2 = 1940$ Correct?
  • · Replies 2 ·
Replies
2
Views
1K
MHB How Can One Demonstrate the Ratio Between the Hypotenuses of Two Triangles?
  • · Replies 2 ·
Replies
2
Views
2K
High School Methods to compute bounds on polynomial roots (not close yet)
  • · Replies 13 ·
Replies
13
Views
2K
High School Understanding Horner's Method: A Brief Explanation for Confusion
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Can New Theorems Predict Incomplete 5x5 Magic Square Solutions?
  • · Replies 68 ·
3
Replies
68
Views
12K
Undergrad ((-8)^2)^(1/3) <> (-8)^(2/3) <> (-8)^(1/3))^2
  • · Replies 6 ·
Replies
6
Views
1K
MHB Evaluate a floor function involving trigonometric functions
  • · Replies 2 ·
Replies
2
Views
3K
MHB How do you factor expressions like 3(x + h)^4 - 48(x + h)^2?
  • · Replies 2 ·
Replies
2
Views
1K
MHB Cot (60°) = 1/tan (60°) = 1/sqrt{3}
  • · Replies 2 ·
Replies
2
Views
1K