Law of Radicals?

Question

please give the laws of radicals and give example for each!!!thank you for answering!
:)

Answer 1

Division of Radical

√7 / 5 =

√7 / √5 =

Rationalized the denominator

√7√5 / √5√5 =

√35 / √25 =

√35 / 5

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Multiplication of Radicals

FOIL

(√2 + √3)(√4 + √6) =

√4√2 + √4√3 + √6√2 + √6√3

2√2 + 2√3 + √12 + √18

2√2 + 2√3 + √4 √3+ √9√2

2√2 + 2√3+ 2√3 + 3√2

Collecting like terms

2√2 + 3√2 + 2√3 + 2√3

2 + 3√2 + 2 + 2 √3

5√2 + 4√3

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Addition of radicals

√27 + √108 + √75

√9√3 + √36√3 + √25√3

3√3 + 6√3 + 5√3

3 + 6 + 5 √3

14√3

people.sunyulster.edu/NicholsM/WebCT/WebCT2/radicals_operations.htm

wtamu.edu/academic/.../mathlab/col_algebra/col_alg_tut4_radical.htm

regentsprep.org/Regents/math/math-topic.cfm?TopicCode=radicals

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Answer 2

I'm not sure what you mean by the law of radicals but I'll give you a few rules in using them.

√a * √b = √(ab)
√a / √b = √(a/b)
√a * √a = √(a*a) = √a² = a

In number theory, the radical of a number is the product of its prime factors where each prime factor is used just once.

So rad(12) = rad(2²*3) = 2*3 = 6

If you are referring to radicals in abstract algebra you need to be more spefic.