Question

Simplificati va rog √(28+16√3)

Answer 1

 

$\displaystyle\bf\\\sqrt{28+16\sqrt{3}}=?\\\\ Avem~radicali~compusi.\\\\16\sqrt{3}=2\times8\sqrt{3}=2\times\underline{4\times2\sqrt{3}}\\\\4^2+(2\sqrt{3})^2=16+12=\underline{28}\\\\unde~\underline{28}=28~de~sub~radical.\\\\\sqrt{28+16\sqrt{3}}=\\\\=\sqrt{16+12+2\times4\times2\sqrt{3}}=\\\\=\sqrt{4^2+(2\sqrt{3})^2+2\times4\times2\sqrt{3}}=\\\\=\sqrt{4^2+2\times4\times2\sqrt{3}+(2\sqrt{3})^2}=\\\\=\sqrt{\Big(4+2\sqrt{3}\Big)^2}=\boxed{\bf4+2\sqrt{3}}$

 

Answer 2

$\sqrt{28 + 16 \sqrt{3} } =$

APLICAM FORMULA RADICALILOR COMPUSI:

a= 28

b= 16•16•3=768

$c = \sqrt{ {28}^{2} - 768}$

$c = \sqrt{16}$

$c = 4$

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

$\sqrt{ \frac{28 + 4}{2} } </em><em>+</em><em> \sqrt{ \frac{28 - 4}{2} }$

$\sqrt{16} </em><em>+</em><em> \sqrt{12}$

$4 </em><em>+</em><em>2 \sqrt{3}$