Square Root of a Quantity of X

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Discussion Overview

The discussion revolves around calculating the square root of a quantity involving a variable, specifically \(\sqrt{25x}\), and the conditions under which the equation \(5x^{2} = 25x\) holds true. Additionally, there are queries regarding manipulating equations to isolate a variable, such as \(y\) in the equation \(\frac{p}{4}=\frac{y}{2}\).

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant asks how to calculate \(\sqrt{25x}\) and whether \(5x^{2}\) can be equated to \(25x\).
  • Another participant suggests that the square root of an unknown \(x\) is simply \(\sqrt{x}\) and states that \(5x^{2} = 25x\) holds true for \(x = 0\) or \(x = 5\).
  • A different participant explains the property of square roots, stating that \(\sqrt{25x} = 5\sqrt{x}\) and clarifies that \(5x^{2}\) and \(25x\) are not identically equal, though they can be equal for specific values of \(x\).
  • Several participants pose additional questions about isolating \(y\) in the equation \(\frac{p}{4}=\frac{y}{2}\), with one suggesting to multiply both sides by 2.

Areas of Agreement / Disagreement

Participants express varying views on the conditions under which \(5x^{2} = 25x\) is valid, with some agreeing on specific values of \(x\) while others clarify that the two expressions are not identically equal. The discussion about isolating \(y\) remains open with multiple participants contributing questions.

Contextual Notes

There are limitations regarding the assumptions about the values of \(x\) and the conditions under which the equations hold. The discussion does not resolve the specific manipulations required for isolating \(y\).

Who May Find This Useful

Students exploring algebraic concepts, particularly those related to square roots and equation manipulation.

MarcAlexander
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How does one calculate the square root of a quantity of x e.g. \sqrt{25x}?

Also could you equate 5x^{2} to 25x?

Just a thew random queries going around my head.

NOTE: I'm 14.
 
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The square root of an unknown (x) is simply another unknown (√x).

You could write 5x2 = 25x. This will hold for x = 0 or x = 5.
 
MarcAlexander said:
How does one calculate the square root of a quantity of x e.g. \sqrt{25x}?
There are properties of square roots that can be used here; namely that for nonnegative real numbers a and b,
\sqrt{ab} = \sqrt{a}\sqrt{b}
So, \sqrt{25x} = \sqrt{25}\sqrt{x} = 5\sqrt{x}
MarcAlexander said:
Also could you equate 5x^{2} to 25x?
mathman already gave an answer to this, but it's worthwhile to find out exactly what you're asking.

When you ask about equating the two quantities, yes, there are a couple of values that make the equation true.

If you're asking whether you can simplify 5x2 to 25x, then no, these two quantities are not identically equal. I'm not sure that this is what you're asking, so I thought I would check.
MarcAlexander said:
Just a thew random queries going around my head.

NOTE: I'm 14.
 
Thanks.
 
Another question.

How would I work out \frac{p}{4}=\frac{y}{2} in terms of y?
 
MarcAlexander said:
Another question.

How would I work out \frac{p}{4}=\frac{y}{2} in terms of y?

What can you do to both sides to get y on its own?

Multiply both sides by 2.
 
FeDeX_LaTeX said:
What can you do to both sides to get y on its own?

Multiply both sides by 2.

Times by 2?
 

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