MHB Is this Fraction Simplified Correctly?

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The discussion revolves around simplifying the expression $\sqrt{5} * \left(\frac{5}{4}\right)^{\frac{1}{2}}$. Participants clarify that $\left(\frac{5}{4}\right)^{\frac{1}{2}}$ can be rewritten as $\frac{\sqrt{5}}{2}$. The simplification leads to the expression $\frac{5^{1/2} \cdot 5^{1/2}}{2}$, which further simplifies to $\frac{5}{2}$. The final consensus confirms that the simplification is correct, resulting in $\frac{5}{2}$. The discussion concludes with affirmation of the correct simplification process.
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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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