Question

tgs T^T
bentuk rasional dari :
[tex] \sf \: \frac{3}{4 - \sqrt{5} } [/tex]
[tex] \sf \: \frac{2 \sqrt{3} }{2 + \sqrt{7} } [/tex]
gunakan cara yang detail kaks agar saya faham ​

Answer 1

Verified answer

BentuK AkaR
RaSional
Akar sekawan

bentuk sederhana dari
a.

[tex]\sf \dfrac{3}{4-\sqrt 5}=[/tex]

[tex]\sf = \left(\dfrac{3}{4-\sqrt 5}\right)\left(\dfrac{4+\sqrt 5}{4+\sqrt5}\right)[/tex]

[tex]\sf = \dfrac{3(4+\sqrt 5)}{(4-\sqrt 5)(4+\sqrt5)}[/tex]

[tex]\sf = \dfrac{3(4+\sqrt 5)}{16- 5}[/tex]

[tex]\sf = \dfrac{3}{11}(4+\sqrt 5)[/tex]

b.
[tex]\sf \dfrac{2\sqrt3}{2+\sqrt7}=[/tex]

[tex]\sf =\left(\dfrac{2\sqrt3}{2+\sqrt7}\right)\left(\dfrac{2-\sqrt7}{2-\sqrt7}\right)[/tex]

[tex]\sf =\dfrac{(2\sqrt3)(2+\sqrt7)}{(2+\sqrt7)(2-\sqrt7)}[/tex]

[tex]\sf =\dfrac{4\sqrt3+ 2\sqrt{21}}{4-7}[/tex]

[tex]\sf =\dfrac{4\sqrt3+ 2\sqrt{21}}{-3}[/tex]