Qual é a raiz quadrada do 156.25?

Responda:

$\sqrt{156.25} = \frac{25}{2}$ $sqrt(156.25) = 25/2$

Explicação:

$15625 = 5^{6}$ $15625 = 5^6$

So $156.25 = \frac{5^{6}}{100} = \frac{5^{6}}{2^{2} \cdot 5^{2}} = \frac{5^{4}}{2^{2}}$ $156.25 = (5^6)/100 = (5^6)/(2^2*5^2) = 5^4/2^2$

If $a, b \geq 0$ $a, b >= 0$ , Em seguida $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ $sqrt(a/b) = sqrt(a)/sqrt(b)$

If $a, b, c > 0$ $a, b, c > 0$ então $a^{b c} = {(a^{b})}^{c}$ $a^(bc) = (a^b)^c$

So $\sqrt{156.25} = \sqrt{\frac{5^{4}}{2^{2}}} = \frac{\sqrt{5^{4}}}{\sqrt{2^{2}}} = \frac{\sqrt{{(5^{2})}^{2}}}{\sqrt{2^{2}}} = \frac{5^{2}}{2} = \frac{25}{2}$ $sqrt(156.25) = sqrt(5^4/2^2) = sqrt(5^4)/sqrt(2^2) = sqrt((5^2)^2)/sqrt(2^2) = 5^2/2 = 25/2$