Question

va rog frumos!
Arata ca numarul a = $2^{5}$ * $3^{7} * 6^{3}$ este patrat perfect, apoi calculeaza $\sqrt{a}$

Answer 1

Răspuns:

a=2⁵·3⁷·6³

a=2⁵·3⁷·(2·3)³

a=2⁵·3⁷·2³·3³

a=2⁵⁺³·3⁷⁺³

a=2⁸·3¹⁰

a=(2²)⁴·(3²)⁵

a=(2⁴·3⁵)²

a=(16·243)²=3888² este pp

√a=3888

Answer 2

$\it a=2^5\cdot3^7\cdot6^3=2^5\cdot3^7\cdot2^3\cdot3^3=2^8\cdot3^{10}=(2^4)^2\cdot(3^5)^2=(2^4\cdot3^5)^2$

$\it \sqrt{a}=\sqrt{(2^4\cdot3^5)^2}=2^4\cdot3^5=16\cdot243$