Question

O número 3√8+4√18-√27-3√48-2√98 é igual a: A)10√2-9√3
B)14√2-15√13
C)18√2-29√3
D)4√2-15√3

Answer 1

3√8 = 3 . $\sqrt{4.2} = 3. \sqrt{4} . \sqrt{2} = 3. 2 \sqrt{2} = 6 \sqrt{2}$

4√18 = 4. $\sqrt{9 . 2} = 4. \sqrt{9} . \sqrt{2} = 4 . 3 . \sqrt{2} = 12 \sqrt{2}$

-√27 = $-1 . \sqrt{9.3} = -1. \sqrt{9} . \sqrt{3} = -1 . 3 . \sqrt{3} = -3 \sqrt{3}$

-3√48 =
Vamos dividir o 48 : $\frac{48}{2} = 24/ \frac{24}{2} = 12/\frac{12}{2} = 6/ \frac{6}{2} = 3$$/ \frac{3}{3} = 1$ então 48 = 2² . 2² . 3

-3 . $\sqrt{2^2.2^2.3} = -3. \sqrt{2^2} . \sqrt{2^2} . \sqrt{3} = -3 . \sqrt{4}. \sqrt{4}. \sqrt{3} = -3 . 2 . 2 . \sqrt{3} = -12 \sqrt{3}$

 -2√98 =
Vamos dividir o 98: $\frac{98}{2} = 49/ \frac{49}{7} = 7/ \frac{7}{7} = 1$ então 98 = 2. 7²

- 2 . $\sqrt{2. 7^2} = -2 . \sqrt{2} . \sqrt{7^2} = -2 . \sqrt{2} . \sqrt{49} = -2 . 7 . \sqrt{2} = -14 \sqrt{2}$

Somando tudo, fica: $6 \sqrt{2} + 12 \sqrt{2} -3 \sqrt{3} -12 \sqrt{3} -14 \sqrt{2}$

Isso dá:
$4 \sqrt{2} - 15 \sqrt{3}$ --> Letra D)

Answer 2

= 3√8 + 4√18 - √27 - 3√48 - 2√98

= 3.√4.√2 + 4√9.√2 - √9.√3 - 3√16.√3 - 2.√49.√2

= 3.2√2 + 4.3√2 - 3√3 - 3.4√3 - 2.7√2

= 6√2 + 12√2 - 3√3 - 12√3 - 14√2

= 18√2 - 15√3 - 14√2

= 4√2 - 15√3 (letra D)