Question

simplifique as expressoes

a) √180 + √500

b) √6 + √24 + √54

Answer 1

a) $\sqrt{180}+ \sqrt{500}$ =

Decompondo 180 e 500 em fatores primos:

180 |2           500 |2
 90 |2            250 |2
 45 |3            125 |5
 15 |3              25 |5
   5 |5                5 |5
                         1

Então 180 = $2^{2}. 3^{2}.5$

          500 = $2^{2}. 5^{2}.5$

$\sqrt{180}+ \sqrt{500}$ =

$\sqrt{ 2^{2}.3^{2}.5}+ \sqrt{ 2^{2}. 5^{2}.5 }$ =

2.3.$\sqrt{5}$ + 2.5.$\sqrt{5}$ =

6$\sqrt{5}$ + 10$\sqrt{5}$ =

16$\sqrt{5}$

b) $\sqrt{6}+ \sqrt{24}+ \sqrt{54}$ =

$\sqrt{6}+ \sqrt{6.4}+ \sqrt{6.9}$ =

$\sqrt{6}+2 \sqrt{6}+3 \sqrt{6}$ =

$6 \sqrt{6}$