Question

1)Usando a decomposição em fatores, primos, calcule a raiz dos números abaixo:

A)√2304= C)√1764=

B)√676= D)√2500=

E)√529= F)√3025=

G)√1024= H)√6562=


2)Calcule a raíz decompondo-a:

A)3√1728= C)3√5832

B)3√10648= D)3√27000=

Quero a conta montada :V

Answer 1

a)

2304|2

1152|2

576|2

288|2

144|2

72|2

36|2

18|2

9|3

3|3

$\boxed{\boxed{\mathsf{ \sqrt{2304} = \sqrt{ {2}^{8}. {3}^{2}} = {2}^{4}.3 = 48}}}$b)

$676={2}^{2}.{13}^{2}$

$\boxed{\boxed{\mathsf{ \sqrt{676} = \sqrt{ {2}^{2}. {13}^{2} } = 2.13 =26 }}}$

c)

$1764={2}^{2}.{3}^{2}.{7}^{2}$

$\boxed{\boxed{\mathsf{ \sqrt{1764} } = \sqrt{ {2}^{2}. {3}^{2}. {7}^{2}} = 2.3.7 = 42}}$

d)

$2500={2}^{2}.{5}^{4}$

$\boxed{\boxed{\mathsf{ \sqrt{2500} = \sqrt{ {2}^{2}. {5}^{4}} = 2. {5}^{2} = 50 }}}$

e)

$529={23}^{2}$

$\boxed{\boxed{\mathsf{ \sqrt{529} } = \cancel{\sqrt{ {23}^{ \cancel2}} } = 23}}$

f)

$3025={5}^{2}.{11}^{2}$

$\boxed{\boxed{\mathsf{ \sqrt{3025} } = \sqrt{ {5}^{2}. {11}^{2} } = 5.11 = 55}}$

g)

$1024={2}^{10}$

$\boxed{\boxed{\mathsf{ \sqrt{1024} = \sqrt{ {2}^{10} } = {2}^{5} = 32}}}$

h) 6562 não é um quadrado perfeito portanto sua raiz quadrada não é exata.

2)

1728|2

864|2

432|2

216|2

108|2

54|2

27|3

9|3

3|3

1

$1728={2}^{6}. {3}^{2}. 3$

$\boxed{\boxed{\mathsf{ \sqrt{1728} = \sqrt{ {2}^{6} .2. {3}^{2} } = {2}^{3} .3 \sqrt{2} }}} \\ =\boxed{\boxed{\mathsf{24 \sqrt{2} }}}$

$\boxed{\boxed{\mathsf{3 \sqrt{1728} = 3.24 \sqrt{2} = 72 \sqrt{2} }}}$

b)

10648|2

5324|2

2662|2

1331|11

121|11

11|11

1

$10648={2}^{2}.2.{11}^{2}.11$

$\boxed{\boxed{\mathsf{ \sqrt{10648} = \sqrt{ {2}^{2}.2. {11}^{2}.11} } }} = \\ \boxed{\boxed{\mathsf{22 \sqrt{22} }}}$

$\boxed{\boxed{\mathsf{3 \sqrt{10648} = 3.22 \sqrt{22} = 66 \sqrt{22} }}}$

c)

5832|2

2916|2

1458|2

729|3

243|3

81|3

27|3

9|3

3|3

1

$5832={2}^{2}.2.{3}^{6}$

$\boxed{\boxed{\mathsf{ \sqrt{5832} = \sqrt{ {2}^{2}.2. {3}^{6}} = 2. {3}^{3} \sqrt{2}} }} \\ = \boxed{\boxed{\mathsf{54 \sqrt{2} }}}$

$\boxed{\boxed{\mathsf{3 \sqrt{5832} = 3.54 \sqrt{2} = 162 \sqrt{2} }}}$

d)

$27000={30}^{3}={2}^{2}.{3}^{2}.3.{5}^{2}$

$\boxed{\boxed{\mathsf{ \sqrt{27000} = \sqrt{ {2}^{2}. {3}^{2} .3. {5}^{2} }}}} \\ = \boxed{\boxed{\mathsf{2.3.5 \sqrt{3} = 30 \sqrt{3} }}}$

$\boxed{\boxed{\mathsf{3 \sqrt{27000} = 3.30 \sqrt{3} = 90 \sqrt{3} }}}$