Add or subtract

Question

Add or subtract . Simplify answer 

 

5√75 -4√50 + √48 =

Answer 1

 The idea is Use " Fundamental Arithmetic Theorem"

 

   Convert every composite number to the product of its prime factors:

 

      75 = 2 * 5²

       √75 = √ ( 2 * 5² ) = √2 * √5² = 5 √2

 

        You can multiply and divide roots( square roots), to have an answer in the form of square roots with

           the product and quotient of the 2 values.

     

        However, only like radicals add up by adding their multipliers.

 

       

Answer 2

I hope the following is what you're looking for:

5√75 = 5√(3*25) = 5√3*√25 = 5*5*√3 = 25*√3

4√50 = 4√(2*25) = 4√2*√25 = 4*5*√2 = 20*√2

√48 = √(4*4*3) = √4*√4*√3 = 4√3

 

Thus: 

5√75 -4√50 + √48 = 25√3 - 20√2 + 4√3

                            = 29√3 - 20√2

Answer 3

 

5√75 -4√50 + √48 = take this equation and break them into perfect square factors.

5√(25*3) -4√(25*2) + √(16*3)  Perfect square can come out see below for the rules

5*5√3 -4*5√2 + 4√3 

25√3 -20√2 + 4√3   Now you can old add / subtract the front value with the same radical value(√)

(25+4)√3 -20√2  Simplify

 

29√3 -20√2  Simplest form

 

 

RULES FOR PERFECT SQUARE

1^2 = 1 & √1 = 1
2^2 = 4 & √4 = 2
3^2 = 9 & √9 = 3
4^2 = 16 & √16 = 4
5^2 = 25 & √25 = 5
6^2 = 36 & √36 = 6
7^2 = 49 & √49 = 7
8^2 = 64 & √64 = 8
9^2 = 81 & √81 = 9
10^2 = 100 & √100 = 10
11^2 = 121 & √121 = 11
12^2= 144 & √144 = 12
13^2 = 169 & √169 = 13
14^2 = 196 & √196 = 14
15^2 = 225 & √225 = 15
20^2 = 400 & √400 = 20

Answer 4

5√75-4√50+√48=5√(3*25)-4√(2*25)+√(3*16)=25√3-20√2+4√3=29√3-20√2

 

Answer: 29√3-20√2