Question

Simplifique os radicais A)-√20 + √125 B)9√2 - √50 C)-5√20 + √32 + 4√45 - √50 D)15√3 + √27 E)√75 - √12

Answer 1

$A) \\ - \sqrt{20} + \sqrt{125} = \\ - \sqrt{2^2.5} + \sqrt{5^2.5} = \\ -2 \sqrt{5} +5 \sqrt{5} = \\ 3 \sqrt{5} \\ \\ B) \\ 9 \sqrt{2} - \sqrt{50} = \\ 9 \sqrt{2} - \sqrt{2.5^2} = \\ 9 \sqrt{2} -5 \sqrt{2} = \\ 4 \sqrt{2}$ 

$C) \\ -5 \sqrt{20} + \sqrt{32} +4 \sqrt{45} - \sqrt{50} = \\ -5 \sqrt{2^2.5} + \sqrt{2^4.2} +4 \sqrt{3^2.5} - \sqrt{2.5^2} = \\ \\ -5.2 \sqrt{5} +4 \sqrt{2} +4.3 \sqrt{5} -5 \sqrt{2} = \\ -10 \sqrt{5} +4 \sqrt{2} +12 \sqrt{5} -5 \sqrt{2} = \\ \\ -10 \sqrt{5} +12 \sqrt{5} +4 \sqrt{2} -5 \sqrt{2} = \\ 2 \sqrt{5} - \sqrt{2}$ 

$E) \\ \sqrt{75} - \sqrt{12} = \\ \sqrt{3.5^2} - \sqrt{2^2.3} = \\ 5 \sqrt{3} -2 \sqrt{3} = \\ 3 \sqrt{3}$

$D) \\ 15 \sqrt{3} + \sqrt{27} = \\ 15 \sqrt{3} + \sqrt{3^2.3} = \\ 15 \sqrt{3} +3 \sqrt{3}= \\ 18 \sqrt{3}$