confusion over how √2√3 / 4 - √2 / 4 simplifies to √2(√3 - 1) / 4 (1st post here!)

[zknox1411]

confusion over how √2√3 / 4 - √2 / 4 simplifies to √2(√3 - 1) / 4 (1st post here!)

apologies for this simple question, but i'm confused over how:

√2√3 / 4 - √2 / 4 simplifies to √2(√3 - 1) / 4

doing the subtraction myself I came up with √6 / 4 - √2 / 4, not sure how one would end up with √2(√3-1) / 4.

I must be ignorant to some principle of subtracting fractions with roots in the numerator or something, thanks.

 

[tkhunny]

apologies for this simple question, but i'm confused over how:

√2√3 / 4 - √2 / 4 simplifies to √2(√3 - 1) / 4

doing the subtraction myself I came up with √6 / 4 - √2 / 4, not sure how one would end up with √2(√3-1) / 4.

I must be ignorant to some principle of subtracting fractions with roots in the numerator or something, thanks.

This principle is used twice:

ab + ac = a(b+c)
or this
bd + cd = (b+c)d

In each case, it is the Distributive Property of Multiplication over Addition.

 

[Dr.Peterson]

apologies for this simple question, but i'm confused over how:

√2√3 / 4 - √2 / 4 simplifies to √2(√3 - 1) / 4

doing the subtraction myself I came up with √6 / 4 - √2 / 4, not sure how one would end up with √2(√3-1) / 4.

I must be ignorant to some principle of subtracting fractions with roots in the numerator or something, thanks.

What they are doing is to factor out √2 / 4 from each term.

Note that the way to add or subtract radical expressions is to simplify each of them, and then combine "like terms". It does not involve factoring. What you did is what we would typically call simplification; what they did is something else!

If the exercise said to simplify, then your answer is correct; but if they didn't mention simplifying, but this is just a step in some other process, then they probably did what they saw as useful for their goal, whatever it was.

The important thing is that their result is equivalent to the original.

Can you show us the context of your question -- the actual statement of the problem, and what else was done?

 

[Steven G]

apologies for this simple question, but i'm confused over how:

√2√3 / 4 - √2 / 4 simplifies to √2(√3 - 1) / 4

doing the subtraction myself I came up with √6 / 4 - √2 / 4, not sure how one would end up with √2(√3-1) / 4.

I must be ignorant to some principle of subtracting fractions with roots in the numerator or something, thanks.

What you did was rewrite √2√3 as √6 which IS correct. What the author did was first factor out the √2 / 4. Personally I do not know which is better to do!