Please come to this question--square roots, so they can be displayed as an equation. Please come to this question--square roots, so they can be displayed as an equation. @Mathematics

Question

anonymous · Answer

$$\sqrt{xy^2z^3}+\sqrt{9xy^2z^3}$$

anonymous · Answer

$$4y \sqrt{xz ^{3}}$$

turingtest · Answer

what do you mean "as an equation" if it's not already got an equals sign all you can do is simplify.

ashish56 · Answer

$$4yz \sqrt{xz}$$

anonymous · Answer

Yeah, i know thats the answer, but idk how they got it. :/

turingtest · Answer

$$\sqrt{xy^2z^3}+\sqrt{9xy^2z^3}=y \sqrt{xz^3}+3y \sqrt{xz^3}=4y \sqrt{xz^3}$$

turingtest · Answer

We took the square root of y^2 and pulled the y out of the radical in the first term.
We did the same and also took the square root of 3 out of the second term. 
Then just combine like terms (which you should notice these are).

anonymous · Answer

Can't you also take out the z^2 from both? And have a z left in the sqrt? Where did the 4 come from? the answer is $$4yz \sqrt{xz}$$ not$$4yz \sqrt{xz^3}$$

ashish56 · Answer

yes you can

turingtest · Answer

yeah, sorry i just spaced out on that one :/

ashish56 · Answer

as there are $$z \times z \times z$$

anonymous · Answer

So the next step would be...$$yz \sqrt{xz}+3yz \sqrt{xz}$$ whats next?

turingtest · Answer

the four came from combining the like terms. let's say$$ yz \sqrt{xz}=p$$then we can write above $$p+3p=4p$$now substitute back expression for p $$ 4yz \sqrt{xz}=p$$

anonymous · Answer

Okay, thanks now i get the 4. But adding the y's and z's... wouldn't you get y^2/z^2?

turingtest · Answer

The y's and the z's do not get added. You seem to have difficulty combining like terms (those containing the same variables multiplied together); perhaps some examples will help:$$4x^2y+7x^2y=11x^2y$$$$3xy^3z^2-xy^3z^2=2xy^3z^2$$$$4xy+5xy+3xz=9xy+3xz$$$$3y+5y^2-y=2y+5y^2$$Notice only the coefficients (the numbers in front of the variables) get added. We do not touch the variables when adding (or subtracting) expressions like those above.

Also notice that in the third example above we could only add the terms containing xy:$$4xy+5xy=9xy$$i.e. we had to leave the 3xz term as it was. 

Why? Because it is NOT a like term; it does not contain xy, but xz instead.

The same goes for the fourth example above; y^2 and y are NOT like terms, so they cannot be added together. Only the coefficients of the y's (not raised to the second power) were combined.

The moral of the story: when you have like terms in an expression that are to be added together, all you combine are their coefficients (the numbers in front) you DO NOT TOUCH THE VARIABLES.