How Do You Simplify 4√(sin(π/4))?

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Discussion Overview

The discussion revolves around simplifying the expression 4√(sin(π/4)). Participants explore various methods and steps involved in the simplification process, seeking clarity on how to arrive at the final result without relying on technology.

Discussion Character

  • Mathematical reasoning
  • Exploratory
  • Homework-related

Main Points Raised

  • One participant expresses difficulty in simplifying 4√(sin(π/4)) and provides their intermediate steps, indicating they feel stuck at a certain point.
  • Another participant suggests that 2√{2} can be rewritten as √{8}, leading to an alternative interpretation of the expression as two times the quartic root of 8.
  • A different participant confirms that they also arrive at √{8} during their calculations and attempts to clarify their reasoning, showing a progression of steps leading to 2√{2√{2}}.
  • One participant connects the quartic root of 8 to an exponent form, stating it simplifies to 2 to the three-fourths power, which aligns with the earlier calculations.
  • A later reply acknowledges the helpfulness of the previous contributions, indicating a realization of the simplification process.
  • Another participant reiterates their initial struggle with the problem, sharing their steps and emphasizing the importance of understanding exponent rules in the simplification process.

Areas of Agreement / Disagreement

Participants present various approaches to the simplification, with no consensus on a single method. Multiple interpretations and steps are discussed, indicating that the discussion remains unresolved regarding the most straightforward path to the solution.

Contextual Notes

Some participants reference intermediate steps and transformations that depend on specific mathematical properties, such as exponent rules, but these steps are not universally agreed upon or fully resolved.

2h2o
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I've come across this before, but for the life of me can't seem to get anywhere with it. I can plug this into technology and get an answer (and then move on...), but I want to know how to do it without.

An example problem:

[tex]4\sqrt{\sin(\pi/4)}[/tex]

I get as far as

[tex]2\sqrt{2\sqrt{2}} = 2(2(2)^\frac{1}{2})^\frac{1}{2}[/tex]

but then I run out of steam and don't see the next step. Surely it is something simple that I am missing, but I just don't see it.

Thanks for any tips. Cheers!
 
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I don't know what you're asking, but since [tex]2\sqrt{2}=\sqrt{8}[/tex], it equals two times the quartic root of 8...
 
I have [tex]\sqrt{8}[/tex] as an intermediate step in my work.

[tex] <br /> 4\sqrt{\sin(\pi/4)} = \sqrt{\frac{16\sqrt{2}}{2}} = \sqrt{8\sqrt{2}} = \sqrt{4*2\sqrt{2}} = 2\sqrt{2\sqrt{2}}<br /> [/tex]

When I plug into technology, I get the answer:

[tex] <br /> 2*2^\frac{3}{4}<br /> [/tex]

but I don't know how to get there. That's what I'm asking; sorry for being unclear.
 
Well, yeah.

Going with my two times quartic root of 8 solution, since 8 is 2 cubed, the quartic root of 8 is 2 to the three-fourths power, and the number simplifies to your number.
 
Of course. Thank you very much! I definitely should've seen that! :)

Cheers.
 
2h2o said:
I've come across this before, but for the life of me can't seem to get anywhere with it. I can plug this into technology and get an answer (and then move on...), but I want to know how to do it without.

An example problem:

[tex]4\sqrt{\sin(\pi/4)}[/tex]

I get as far as

[tex]2\sqrt{2\sqrt{2}} = 2(2(2)^\frac{1}{2})^\frac{1}{2}[/tex]

but then I run out of steam and don't see the next step. Surely it is something simple that I am missing, but I just don't see it.

Thanks for any tips. Cheers!

When you multiply a two numbers with the same base, the exponents add. So,

[tex]2(2^{1}*2^{\frac{1}{2}})^{\frac{1}{2}} = 2(2^{1+\frac{1}{2}})^{\frac{1}{2}} = 2(2^{\frac{3}{2}*\frac{1}{2}}) = 2*2^{\frac{3}{4}}[/tex]
 

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