Question

Calcule o valor decimal de X em anexo:

Answer 1

Resposta:

Solução:

$\sf X = \displaystyle \sqrt{25\;000\cdot (0,0004) \cdot 32}$

$\sf X = \sqrt{25\:000} \: \cdot \sqrt{0,0004} \: \cdot\sqrt{32}$

$\sf \displaystyle X = 50 \cdot \sqrt{10} \: \cdot 0,02 \cdot 4\cdot \sqrt{2}$

$\sf \displaystyle X = (50 \cdot 0,02 \cdot 4) \cdot \sqrt{10} \:\cdot \sqrt{2}$

$\sf \displaystyle X = 4 \cdot \sqrt{20}$

$\sf \displaystyle X = 4 \cdot \sqrt{4 \cdot 5}$

$\sf \displaystyle X = 4 \cdot \sqrt{4} \cdot \sqrt{5}$

$\sf \displaystyle X = 4 \cdot 2 \cdot 17,84$

$\boxed{ \boxed { \boldsymbol{ \sf \displaystyle X =142.72 }}} \quad \gets \mathbf{ Resposta }$

Explicação passo-a-passo:

$\sf \displaystyle \sqrt{25\:000} = \sqrt{25 \cdot 1000} = \sqrt{25 \cdot 100 \cdot 10} = \sqrt{25} \cdot \sqrt{100}\: \cdot \sqrt{10}$

$\sf \displaystyle \sqrt{25\:000} =5 \cdot 10 \cdot \sqrt{10}$

$\sf \displaystyle \sqrt{25\:000} = 50 \cdot \sqrt{10}$

$\sf \displaystyle \sqrt{0,0004} = 0,02$

$\sf \displaystyle \sqrt{32} = \sqrt{16 \cdot 2} = \sqrt{16} \cdot \sqrt{2}$

$\sf \displaystyle \sqrt{32} = \sqrt{16 \cdot 2} = 4\cdot \sqrt{2}$