so how do you subtract?

Question

surds..

is there any rules when u subtract surds?

what would

√40 - √8 be?

pls explain in detail

what would √25 - √16 be?

pls explain in detail

what would 3√2 + 5√2 be?

pls explain in detail

and in questions like that, do you just add whatever is on the outside?(in this case 3 and 5)-why/why not

and what would

5√3 + 2√5 - 3√3 -7√5 be?

pls explain in detail.


best answer goes to first answer that explains in detail and is easy 4 me 2 understand. if the 1st person has answerd dont think that they will get best A for sure coz they probably didnt explain it well enough

so pls answer those questions and answer in detail.

thanks!!

best answer is waiting 4 you

RustyL71

good answer!

in 5√3 + 2√5 - 3√3 -7√5, 5√3-3√3= 2√3

(can you subtract the 3s under the square root?-why/why not?)

and in 5√3 + 2√5 - 3√3 -7√5:
i understand the 5√3 - 3√3=2√3, but the 2√5 appears before the 7√5, so shouldn't the answer be:

2√3 + (2√5-7√5)

= ......

??

also IS there such thing as -5√3 , for example?

sorry im just a bit confused

btw, they are all great answers so far!!

:-)

thanks!

i really cant choose just one best answer because they're all so great!

thanks for all the help. im putting this question to vote because you all helped me so much and all your answers were great!

Thanks to all!!

Answer 1

√25 - √16 = 5 - 4 = 1

3√2 + 5√2 = 8√2

5√3 - 3√3 + 2√5 - 7√5
2√3 - 5√5

Hope you can follow this---I`m sure you can.

Answer 2

By saying "just add whatever is on the outside," it implies you are not learning maths, but pattern recognition. Thus you asked for "detail explanation" because these patterns are more complex than the earlier ones that you have come across.

Then, some "detail explanations" you couldn't follow because those are the mathematical ones, while you expect pattern-recognitional ones.

My advice is you have to quickly stop and forget all those "pattern-recognitional" maths that you have learnt. Start learning maths the mathematical ways.

"just add whatever is on the outside" in maths involves factorisation, or applying the distributive properties of multiplication over addition and subtraction:
3√2 + 5√2 = 3*√2 + 5*√2 = (3 + 5)*√2
The first step of factorisation is skipped in this case because already the common factor is √2 obviously and clearly.

For the first question, you just need to find the common factor.
√40 - √8 = √(8*5) - √8 = √8√5 - √8 = (√8)*(√5 - 1)
That's it. You may do further steps but that's not necessary unless the question specifically said so:
(√8)*(√5 - 1) = (√(4*2))*(√5 - 1) = (2√2)*(√5 - 1)

This is a special case since 25 and 16 are perfect squares:
√25 - √16 = 5 - 4 = 1

5√3 + 2√5 - 3√3 -7√5 can be simplified similar to 3√2 + 5√2

As a matter of fact:
5*3 + 2*5 - 3*3 - 7*5
= 5*3 - 3*3 + 2*5 - 7*5
= (5 - 3) * 3 + (2 - 7) * 5
= 2 * 3 - 5 * 5

Yes, the above expressions represent the value 19, but in maths, knowing the value represented is less important as compared to knowing the above expressions have the same value.

Please learn factorisation, or applying the distributive properties of multiplication over addition and subtraction. In maths, I think there shouldn't be a topic or lesson on surd subtraction!

Answer 3

5

Answer 4

For addition and subtraction of square roots, if the square root is the same in each number, then you can add the numbers outside of the square root together to get your answer. For example: 3√2 + 5√2 = 8√2, since √2 is in each number.

The same works for subtraction: 8√2 - 5√2 = 3√2.

In the lower example you gave, the √3 numbers and √5 numbers can be combined so that you have the following:

5√3 + 2√5 - 3√3 - 7√5 = 2√3 - 5√5.

In your top examples, the key is to simplify the square root as much as possible. For example, the square root of 25 is 5, and the square root of 16 is 4, so:

√25 - √16 = 5 - 4 = 1.

With √40 - √8, you would want to find multiples of each number that you could pull outside of the square root sign. For example √8 is the same as √(4*2), and the square root of 4 is 2, so √8 is the same as 2√2. Unfortunately, I don't think √40 - √8 simplifies down very far, so you're left with:

√40 - √8 = √(4*10) - √(4*2) = 2√10 - 2√2.

Hope that helps out.

Answer 5

Treat the radicand, or the number or expression under the radical, as a variable. For instance, 3√5 + 2√5 is like 3x + 2x, or 5x. So, combine the exponents algebraically, 3√5 + 2√5, or 5√5. Same with subtraction.

√40 - √8 would be like saying x - y. You can't go any farther.

The basic law of surds:
√a x √b = √ab
√a / √b = √(a/b)

Sometimes you can simplify the radicand:
√20 - √5
√(4 x 5) - √5
(√4 x √5) - √5
2√5 - √5
√5

Answer 6

In order to add or subtract surds, you have to have a common number in the actual surd.

√40 - √8 really equals √40-8
√25 - √16 really equals √25-16
3√2 + 5√2 really equals 8√2
5√3 + 2√5 - 3√3 -7√5 really equals 2√3 - 5√5

I am about 99% sure these are correct. I hope that you find this helpful!

Answer 7

I'll do two of them for you so you can see the method.

sqrt(40) - sqrt(8) = sqrt(4 * 10) - sqrt(2 * 4) = 2 sqrt(10) - 2 sqrt(2)

sqrt(25) - sqrt(16) = sqrt(5 * 5) - sqrt(4 * 4) = 5 - 4 = 1

Get the idea?