Square Root of a Quantity of X

1. Sep 24, 2011

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.

2. Sep 24, 2011

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.

3. Sep 24, 2011

Staff: Mentor

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, $\sqrt{25x} = \sqrt{25}\sqrt{x} = 5\sqrt{x}$
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.

4. Sep 25, 2011

MarcAlexander

Thanks.

5. Sep 25, 2011

MarcAlexander

Another question.

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

6. Sep 25, 2011

FeDeX_LaTeX

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

Multiply both sides by 2.

7. Sep 25, 2011

Times by 2?