# Some maths problem

IB
Suppose I have sqrt (a^2 - a [delta] d). What do I do? Do I do like this: sqrt (a^2 - a [delta] d) = a - sqrt(a [delta] d)? Thanks.

PS: One more thing. How to write mathematics with latex?

Learning Curve
What is sqrt (a^2 - a [delta] d) equal to? or are you asking to simplify it?

IB
Yeah. I was just wondering whether it can still be simplified.

Staff Emeritus
Gold Member
Depending on what you want to do, a differential approximation, or maybe a Taylor sum, might be useful.

But as for algebraic manipulation, what you did is wrong. roots and exponents (usually) distribute over multiplication (and division), not addition (and subtraction).

IB
Hurkyl said:
But as for algebraic manipulation, what you did is wrong. roots and exponents (usually) distribute over multiplication (and division), not addition (and subtraction).

Could you give an example to demonstrate that? And how can I correct my wrong algebraic manipulation? Thanks.

Homework Helper
Say a = 5, and delta d = 9 / 5.
So:
$$\sqrt{a ^ 2 - a \Delta d} = \sqrt{5 ^ 2 - 5 \times \frac{9}{5}} = \sqrt{25 - 9} = \sqrt{16} = 4$$
And:
$$a - \sqrt{a \Delta d} = 5 - \sqrt{5 \times \frac{9}{5}} = 5 - \sqrt{9} = 5 - 3 = 2$$
And 4 is not 2.
Viet Dao,

IB
Thanks, VietDao29.