Question

o valor da expressão √240+√180-√60 é

Answer 1

$\large\textsf{Vamos L\'a:}$

$\sqrt{240} \ + \ \sqrt{180} \ - \ \sqrt{60}$

$\large\textbf{Vamos fatorar cada um separadamente.}$

$240/2 \\\ 120/2 \\\ 60/2 \\\ 30/2 \\\ 15/3 \\\ 5/5 \\\ 1/$

$\boxed{= 4 \sqrt{15} }$
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$180/2 \\\ 90/2 \\\ 45/5 \\\ 9/3 \\\ 3/3 \\\ 1/$

$\boxed{= 6 \sqrt{5} }$

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$60/2 \\\ 30/2 \\\ 15/3 \\\ 5/5 \\\ 1/$

$\boxed{= 2 \sqrt{15} }$

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$\sqrt{240} \ + \ \sqrt{180} \ - \ \sqrt{60}$

$(4 \sqrt{15})+(6 \sqrt{5}) \ - \ (2 \sqrt{15})$
$(4 \sqrt{15})\ - \ (2 \sqrt{15}) \ + \ (6 \sqrt{5})$
$(2 \sqrt{15}) \ + \ (6\sqrt{5})$

$" colocando \ o \ 2 \ em \ evid\^encia"$

$2*( \sqrt{15}\ + \ 3 \sqrt{5})$


$\large\textbf{Resposta Final: \boxed{\mathsf{2 \ * (\sqrt{15} \ + \ 3\sqrt{5}) \ }}}$

Espero Ter Ajudado!!!
Bons Estudos!!!
;D

Answer 2

= √240 + √180 - √60
= √16.√15 + √36.√5 - √4.√15
= 4√15 + 6√5 - 2√15
= 4√15 - 2√15 + 6√5

= 2√15 + 6√5

= 2(√15 + 3√5)

Resp.: 2(√15 + 3√5)

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240: 2
120: 2
60: 2
30: 2
15: 3
5: 5
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1  = 2⁴.3.5  = √16.√3.√5 = 4√15

180: 2
90: 2
45: 3
15: 3
5: 5
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1   =   2².3².5 = √2².√3².√5 = 2.3√5 = 6√5

60: 2
30: 2
15: 3
5: 5
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1  =  2².3.5 = √4.√3.√5 = 2√15