Tentukan hasil operasi bilangan – bilangan berikut ini!

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1.(√5 + √3)pangkat 2
2.(2√2 – √5)pangkat 2
3.(2√3 – 4)pangkat 2

Tentukan hasil operasi bilangan – bilangan berikut ini!

Jawaban Terkonfirmasi

Inget bentuk aljabar ini:
(a+_b)^2 = (a^2) + (b^2) +_ 2ab

(sqrt5 + sqrt3) = 5 + 3 + 2.sqrt15 = 8 + 2sqrt15
(2sqrt2 – sqrt5) = 8 + 5 – 2.2sqrt10 = 13 – 4sqrt10
(2sqrt3 – 4) = 12 + 16 – 2.4.2sqrt3 = 28 – 16sqrt3

note: sqrt= akar

Jawaban Terkonfirmasi

$begin{align} left(sqrt5+sqrt3right)^2&=left(sqrt5+sqrt3right)left(sqrt5+sqrt3right)\&=sqrt{25}+sqrt{15}+sqrt{15}+sqrt9\&=5+2sqrt{15}+3\&=boxed{8+2sqrt{15}}end{align}

$begin{align}left(2sqrt2-sqrt5right)^2&=left(2sqrt2-sqrt5right)left(2sqrt2-sqrt5right)\&=4sqrt4-2sqrt{10}-2sqrt{10}+sqrt{25}\&=8-4sqrt{10}+5\&=boxed{13-4sqrt{10}}end{align}

$begin{align} left(2sqrt3-4right)^2&=left(2sqrt3-4right)left(2sqrt3-4right)\&=4sqrt9-8sqrt{3}-8sqrt{3}+16\&=12-16sqrt{3}+16\&=boxed{28-16sqrt3} end{align}