simplifique os raducais e efetue as operações a)√2+√32= b)√27+√3= c)5√5 + 2√20= d)9√2 + 2√50= e)√12 + 9√3 + √27=
Soluções para a tarefa
Resposta:
a) \sqrt{2}+ \sqrt{32}=\sqrt{2}+ 4\sqrt{2}=5\sqrt{2
b)\sqrt{27}+\sqrt{3}=3\sqrt{3}+\sqrt{3}=4\sqrt{3}
27
+
3
=3
3
+
3
=4
3
c) 3\sqrt{5}+\sqrt{20}=3\sqrt{5}+2\sqrt{5}=5\sqrt{5}3
5
+
20
=3
5
+2
5
=5
5
d) \sqrt{27}+5\sqrt{3}=3\sqrt{3}+5\sqrt{3}=8\sqrt{3}
27
+5
3
=3
3
+5
3
=8
3
e) 2\sqrt{7}+\sqrt{28}=2\sqrt{7}+2\sqrt{7}=4\sqrt{7}2
7
+
28
=2
7
+2
7
=4
7
f) \sqrt{50}-\sqrt{98}=5\sqrt{2}-7\sqrt{2}=-2\sqrt{2}
50
−
98
=5
2
−7
2
=−2
2
g) \sqrt{20}-\sqrt{45}=2\sqrt{5}-3\sqrt{5}=-\sqrt{5}
20
−
45
=2
5
−3
5
=−
5
h) \sqrt{28}-10\sqrt{7}=2\sqrt{7}-10\sqrt{7}=-8\sqrt{7}
28
−10
7
=2
7
−10
7
=−8
7
i) 9\sqrt{2}+3\sqrt{50}=9\sqrt{2}+3\sqrt{50}=9\sqrt{2}+3*(5\sqrt{2})=9\sqrt{2}+15\sqrt{2}=24\sqrt{2}9
2
+3
50
=9
2
+3
50
=9
2
+3∗(5
2
)=9
2
+15
2
=24
2
j) 6\sqrt{3}+\sqrt{75}=6\sqrt{3}+5\sqrt{3}=11\sqrt{3}6
3
+
75
=6
3
+5
3
=11
3
k) \sqrt{98}+5\sqrt{18}=\sqrt{98}+5\sqrt{18}=7\sqrt{2}+5(3\sqrt{2})=7\sqrt{2}+15\sqrt{2}=22\sqrt{2}
98
+5
18
=
98
+5
18
=7
2
+5(3
2
)=7
2
+15
2
=22
2
l) 3\sqrt{98}-2\sqrt{50}=3(7\sqrt{2})-2(5\sqrt{2})=21\sqrt{2}-10\sqrt{2}=11\sqrt{2}3
98
−2
50
=3(7
2
)−2(5
2
)=21
2
−10
2
=11
2
m) 3\sqrt{8}-7\sqrt{50}=3(2\sqrt{2})-7(5\sqrt{2})=6\sqrt{8}-35\sqrt{2}=-29\sqrt{2}3
8
−7
50
=3(2
2
)−7(5
2
)=6
8
−35
2
=−29
2
n) 2\sqrt{32}-5\sqrt{18}=2(4\sqrt{2})-5(3\sqrt{2})=8\sqrt{2}-15\sqrt{2}=-7\sqrt{2}2
32
−5
18
=2(4
2
)−5(3
2
)=8
2
−15
2
=−7
2
o) \sqrt{75}-2\sqrt{12}+\sqrt{27}=5\sqrt{3}-2(2\sqrt{3})+3\sqrt{3}=5\sqrt{3}-4\sqrt{3}+3\sqrt{3}=4\sqrt{3}
75
−2
12
+
27
=5
3
−2(2
3
)+3
3
=5
3
−4
3
+3
3
=4
3
p) \sqrt{12}-9\sqrt{3}+\sqrt{75}=2\sqrt{3}-9\sqrt{3}+5\sqrt{3}=-2\sqrt{3}
12
−9
3
+
75
=2
3
−9
3
+5
3
=−2
3
q) \sqrt{98}-\sqrt{18}-5\sqrt{32}=7\sqrt{2}-3\sqrt{2}+5(4\sqrt{2})=7\sqrt{2}-3\sqrt{2}+20\sqrt{2}=24\sqrt{2}
98
−
18
−5
32
=7
2
−3
2
+5(4
2
)=7
2
−3
2
+20
2
=24
2
r) 5\sqrt{180}+\sqrt{245}-17\sqrt{5}=6\sqrt{5}+7\sqrt{5}-17\sqrt{5}=-4\sqrt{5}5
180
+
245
−17
5
=6
5
+7
5
−17
5
=−4
5