# Working out the units?

I am having a problem finding the correct SI unitsfor the quantity A?

In the equation

A=√(R/TY)

That is A equals the square root of R divided by TY

(not to good showing workings on the computer sorry)

, the SI units of the quantity R are kg m^3 s^–2, the SI units of the quantity T are kg and the SI units of the quantity Y are m s^–2. What are the correct SI units for the quantity A?

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## Answers and Replies

Mark44
Mentor
I am having a problem finding the correct SI unitsfor the quantity A?

In the equation

A=√R/TY

That is A equals the square root of R divided by TY
Both your notation and explanation are ambiguous.

Is the expression on the right side this?
$$\sqrt{\frac{R}{TY}}$$
or this?
$$\frac{\sqrt{R}}{TY}$$
(not to good showing workings on the computer sorry)

, the SI units of the quantity R are kg m^3 s^–2, the SI units of the quantity T are kg and the SI units of the quantity Y are m s^–2. What are the correct SI units for the quantity A?

The first one R/ty all square root. Do apologise for the bad format

Then, the units of A are meters.

To clarify gsal's answer...

You have the expression
$$\sqrt{\frac{R}{TY}}$$

Simply, insert the units for each variable (in place of the variables):
$$\sqrt{\frac{\frac{kg\cdot m^3}{s^2}}{(kg)(\frac{m}{s^2})}}$$

and simplify...
$$\sqrt{\left(\frac{kg \cdot m^3}{s^2}\right) \left(\frac{s^2}{kg \cdot m}\right)}$$

kg and s2 cancel out, leaving
$$\sqrt{\frac{m^3}{m}}$$

which is
$$\sqrt{m^2}$$

or, more simply m