Question

Efetue as operações abaixo, simplificando ao máximo o resultado:

a) 2√3 + 3√3 + 10√ 3

b) 5√ 2- 4√2 + 3√ 2

c) √2 + √50 - √ 98+ √ 18

d) √20 - √45 + √5 - √ 80

e) 2√48 + 3 √ 27- √ 75- √3​

Answer 1

a)

$2 \sqrt{3} + 3 \sqrt{3} + 10 \sqrt{3} = 15 \sqrt{3}$

b)

$5 \sqrt{2} - 4 \sqrt{2} + 3 \sqrt{2} = 4 \sqrt{2}$

c)

$\sqrt{2} + \sqrt{50} - \sqrt{98} + \sqrt{18} \\ \sqrt{2} + \sqrt{25 \times 2} - \sqrt{49 \times 2} + \sqrt{9 \times 2} \\ \sqrt{2} + ( \sqrt{25} \times \sqrt{2} ) - ( \sqrt{49} \times \sqrt{2} ) + \sqrt{9} \times \sqrt{2} ) \\ \sqrt{2} + 5 \sqrt{2} - 7 \sqrt{2} + 3 \sqrt{2} \\ 2 \sqrt{2}$

d)

$\sqrt{20} - \sqrt{45} + \sqrt{5} - \sqrt{80} \\ \sqrt{4 \times 5} - \sqrt{9 \times 5} + \sqrt{5} - \sqrt{16 \times 5} \\ ( \sqrt{4} \times \sqrt{5} ) - ( \sqrt{9} \times \sqrt{5} ) + \sqrt{5} - ( \sqrt{16} \times \sqrt{5} ) \\ 2 \sqrt{5} - 3 \sqrt{5} + \sqrt{5} - 4 \sqrt{5} \\ - 4 \sqrt{5}$

e)

$2 \sqrt{48} + 3 \sqrt{27} - \sqrt{75} - \sqrt{3} \\ 2( \sqrt{16 \times 3} ) + 3( \sqrt{9 \times 3} ) - \sqrt{25 \times 3} - \sqrt{3} \\ 2( \sqrt{16} \times \sqrt{3} ) + 3( \sqrt{9} \times \sqrt{3} ) - ( \sqrt{25} \times \sqrt{3} ) - \sqrt{3} \\ 2(4 \sqrt{3} ) + 3(3 \sqrt{3}) - 5 \sqrt{3} - \sqrt{3} \\ 8 \sqrt{3} + 9 \sqrt{3} - 5 \sqrt{3} - \sqrt{3} \\ 11 \sqrt{3}$