Question

deconponha o radicando em fatores primos e retirando do radicando simpifique os radicais√49 √729 3^√80 4^√32

Answer 1

$\sqrt{49}= \sqrt{7^2} =7$

Decompondo o 729 fica:
729/3 = 243
243/3 = 81
81/3 = 27
27/3 = 9
9/3 = 3
3/3 = 1

Logo, $\sqrt{729} = \sqrt{3.3.3.3.3.3} = \sqrt{3^2.3^2.3^2} =3.3.3=27$

$3^{\sqrt{80} }$, vamos decompor o 80

80/2 = 40
40/2 = 20 
20/2 = 10
10/2 = 5
5/5 = 1

logo, $\sqrt{80}= \sqrt{2.2.2.2.5} = \sqrt{2^2.2^2.5} =4 \sqrt{5}$

$3^{\sqrt{80} }=3^{4\sqrt{5} }$

$4^{ \sqrt{32} }$

Decompondo o 32 temos:

32/2 = 16
16/2 = 8
8/2 = 4
4/2 = 2
2/2 = 1

Logo, $\sqrt{32}= \sqrt{2.2.2.2.2}= \sqrt{2^2.2^2.2} = 4 \sqrt{2}$

$4^{ \sqrt{32} }=({2^2})^{4 \sqrt{2} }=2^{8 \sqrt{2} }$