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GameR89
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Simplificati va rog √(28+16√3)

Răspuns :

 

[tex]\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}}[/tex]

 

Dly23

[tex] \sqrt{28 + 16 \sqrt{3} } = [/tex]

APLICAM FORMULA RADICALILOR COMPUSI:

a= 28

b= 16•16•3=768

[tex]c = \sqrt{ {28}^{2} - 768} [/tex]

[tex]c = \sqrt{16} [/tex]

[tex]c = 4[/tex]

[tex] \sqrt{ \frac{a + c}{2} } + \sqrt{ \frac{a - c}{2} } = [/tex]

[tex] \sqrt{ \frac{28 + 4}{2} } + \sqrt{ \frac{28 - 4}{2} } [/tex]

[tex] \sqrt{16} + \sqrt{12} [/tex]

[tex]4 +2 \sqrt{3} [/tex]

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