Question

Determine o valor de √(17- √225) /√(17+ √225)

Answer 1

√(17- √225) /√(17+ √225)
√(17- 15) /√(17+ 15)
√2 /√32 . √32 /√32. Racionalize.
√64 /32 = 8/32. Simplifique por 8.
Logo 1/4.
Espero ter ajudado.

Answer 2

$\dfrac{\sqrt{17-\sqrt{225}}}{\sqrt{17+\sqrt{225}}}$

Lembre-se que $\sqrt{225}=15$, então:

$\dfrac{\sqrt{17-\sqrt{225}}}{\sqrt{17+\sqrt{225}}}=\dfrac{\sqrt{17-15}}{\sqrt{17+15}}=\dfrac{\sqrt{2}}{\sqrt{32}}$

Note que:

$\sqrt{32}=\sqrt{2^5}=\sqrt{2^4\cdot2}=\sqrt{(2^2)^2\cdot2}=2^2\cdot\sqrt{2}=4\sqrt{2}$

Então:

$\dfrac{\sqrt{2}}{\sqrt{32}}=\dfrac{\sqrt{2}}{4\sqrt{2}}=\dfrac{1}{4}$

Logo:

$\dfrac{\sqrt{17-\sqrt{225}}}{\sqrt{17+\sqrt{225}}}=\dfrac{1}{4}$