Question

n=√(21+12√3)
n=?
dau coroana ​

Answer 1

Răspuns:

n = $\sqrt{21+12\sqrt{3} }$

n = $\sqrt{(3+2\sqrt{3)^{2} } }$

n = 3 + $2\sqrt{3}$

Answer 2

Explicație pas cu pas:

$n = \sqrt{21 + 12 \sqrt{3} } = \sqrt{9 + 2 \cdot 3 \cdot 2 \sqrt{3} + 12} = \\ = \sqrt{ {3}^{2} + 2 \cdot 3 \cdot 2 \sqrt{3} + {(2 \sqrt{3} )}^{2} } \\ = \sqrt{{(3 + 2 \sqrt{3} )}^{2}} = |3 + 2 \sqrt{3} | = \bf 3 + 2 \sqrt{3}$