Square Root of a Quantity of X

[MarcAlexander]

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.

 

[mathman]

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.

 

[Mark44]

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}

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.

Just a thew random queries going around my head.

NOTE: I'm 14.

 

[MarcAlexander]

Thanks.

 

[MarcAlexander]

Another question.

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

 

[FeDeX_LaTeX]

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?

Spoiler

Multiply both sides by 2.

 

[MarcAlexander]

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

Spoiler

Multiply both sides by 2.

Times by 2?