Is this Fraction Simplified Correctly?

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Discussion Overview

The discussion revolves around the simplification of the expression $\sqrt{5} * \left(\frac{5}{4}\right)^{\!{\frac{1}{2}}}$. Participants explore the steps involved in simplifying this mathematical expression, focusing on the application of square roots and fractional exponents.

Discussion Character

  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant presents the expression $\sqrt{5} * \left(\frac{5}{4}\right)^{\!{\frac{1}{2}}}$ and seeks confirmation on its simplification.
  • Another participant suggests using the hint that $x^{1/2} = \sqrt{x}$ to simplify the expression further.
  • A subsequent reply shows the transformation of the expression into $5^{1/2} * \frac{5^{1/2}}{2}$, indicating a step in the simplification process.
  • Further simplification leads to the expression $\frac{5^{1/2}\cdot5^{1/2}}{2}$, which is presented as a potential next step.
  • Another participant confirms that this leads to $\frac{\sqrt{5}\cdot\sqrt{5}}{2}=\frac{\sqrt{5}^2}{2}=\frac{5}{2}$, questioning if this is correct.
  • A later reply agrees with the simplification, affirming the result as correct.

Areas of Agreement / Disagreement

While there is a progression in the simplification steps, the discussion does not explicitly resolve whether the initial expression was simplified correctly, as participants focus on the steps rather than a definitive conclusion.

Contextual Notes

The discussion includes various mathematical transformations and relies on the understanding of square roots and exponents, but does not clarify any assumptions regarding the initial expression's simplification.

mathlearn
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$\sqrt{5} * \left(\frac{5}{4}\right)^{\!{\frac{1}{2}}}$

Many Thanks :)
 
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mathlearn said:
$\sqrt{5} * \left(\frac{5}{4}\right)^{\!{\frac{1}{2}}}$

Many Thanks :)
Hint: [math]x^{1/2} = \sqrt{x}[/math]

Can you finish from here?

-Dan
 
topsquark said:
Hint: [math]x^{1/2} = \sqrt{x}[/math]

Can you finish from here?

-Dan

$5^\frac{1}{2} * \frac{5^\frac{1}{2}}{2^2\frac{1}{2}}$

$5^\frac{1}{2} * \frac{5^\frac{1}{2}}{2}$

From there ... (Thinking)
 
$$\frac{5^{1/2}\cdot5^{1/2}}{2}$$

Does that help? (See topsquark's post).
 
greg1313 said:
$$\frac{5^{1/2}\cdot5^{1/2}}{2}$$

Does that help? (See topsquark's post).

According to topsquark $\displaystyle x^{1/2} = \sqrt{x}$

$$\frac{\sqrt{5}\cdot\sqrt{5}}{2}=\frac{\sqrt{5}^2}{2}=\frac{5}{2}$$

Correct?

Many THanks :)
 
mathlearn said:
According to topsquark $\displaystyle x^{1/2} = \sqrt{x}$

$$\frac{\sqrt{5}\cdot\sqrt{5}}{2}=\frac{\sqrt{5}^2}{2}=\frac{5}{2}$$

Correct?

Many THanks :)

Correctomundo! Well done.
 

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