Question

Simplificar as expressões 7√32 - 5√2 + √8 2√150 - 4√54 + 6√24

Answer 1

We try to represent each number inside the square root as a product of a square and another number.

a) 7√32 - 5√2 + √8

√32  = √(16 *2) = √16 * √2  = 4* √2 =  4√2

√8 = √(4 *2) = √4 * √2  = 2* √2 = 2√2

7√32 - 5√2 + √8 = 7*(4√2) - 5√2 + 2√2 =
      
                         = 28√2  - 5√2 + 2√2          Factorize out √2

                           = (28 - 5 + 2)√2  

                          =  25√2      

b)      2√150 - 4√54 + 6√24       

√150 = √(25 * 6) = √25 * √6 = 5*√6 = 5√6

√54 = √(9 * 6) = √9 * √6 = 3*√6 = 3√6

√24 = √(4 * 6) = √4 * √6 = 2*√6 = 2√6


2√150 - 4√54 + 6√24 = 2*(5√6) - 4*(3√6) + 6*(2√6)

                                = 2*5√6 - 4*3√6 + 6*2√6

                                = 10√6  - 12√6 + 12√6        Factorize √6

                               =  (10 - 12 + 12)√6

                               =  10√6

Answer 2

$7 \sqrt{32} - 5 \sqrt{2} + \sqrt{8} \\ \\ 7 \times 4 \sqrt{2} - 5 \sqrt{2} + 2 \sqrt{2} \\ \\ 28 \sqrt{2} - 5 \sqrt{2} + 2 \sqrt{2} \\ \\ 25 \sqrt{2}$

The final result is: 25√2 or 35.3553.

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$2 \sqrt{150} - 4 \sqrt{54} + 6 \sqrt{24} \\ \\ 2 \times 5 \sqrt{6} - 4 \sqrt{54} + 6 \sqrt{24} \\ \\ 2 \times 5 \sqrt{6} - 4 \times 3 \sqrt{6} + 6 \sqrt{24} \\ \\ 2 \times 5 \sqrt{6} - 4 \times 3 \sqrt{6} + 6 \times 2 \sqrt{6} \\ \\ 10 \sqrt{6} - 4 \times 3 \sqrt{6} + 6 \times 2 \sqrt{6} \\ \\ 10 \sqrt{6} - 12 \sqrt{6} + 6 \times 2 \sqrt{6} \\ \\ 10 \sqrt{6} - 12 \sqrt{6} + 12 \sqrt{6} \\ \\ 10 \sqrt{6}$

The final result is: 10√6 or 24.4949.