Question

$\sqrt{8-2\sqrt{15} }$ este egal cu

Answer 1

FORMULA RADICALILOR COMPUȘI:

$\green{ \boxed{ \sqrt{a + \sqrt{b} } = \sqrt{ \frac{a + c}{2} } + \sqrt{ \frac{a - c}{2} } }}$

$\green {\boxed{c = \sqrt{ {a}^{2} - b} }}$

$\sqrt{8 - 2 \sqrt{15} }$

2✓15 = ✓2²•15 = ✓4•15 = ✓60 → b=60

c=✓8²-60 = ✓64-60 = ✓4 =2

$\sqrt{8 - 2 \sqrt{15} } = \sqrt{ \frac{8 + 2}{2} } + \sqrt{ \frac{8 - 2}{2} } = \\ \\ = \sqrt{ \frac{10}{2} } + \sqrt{ \frac{6}{2} } = \sqrt{5} + \sqrt{3}$