Question

Aratati ca urmatoarele nr sunt patrate perfecte :

b) 2^18×3^6
c) 25×3^18
d) 16×100
e) 4^15×121^17
f) 5^14×7^8×13^24
g) 3^25+3^24
h) 2^25-7×2^20​

Answer 1

Răspuns:

Explicație pas cu pas:

$\bf a)~16\cdot25=4^2\cdot5^2= \big(4\cdot5\big)^2=\blue{\underline{20^2=pp}}$

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$\bf b)~2^{18}\cdot3^6=2^{9\cdot2}\cdot3^{3\cdot2}=$

$\bf \big(2^9\big)^2\cdot\big(3^3\big)^2=\green{\underline{\big(2^9\cdot3^3\big)^2=pp}}$

===========================

$\bf c)~25\cdot3^{18}=5^2\cdot3^{9\cdot2}=$

$\bf 5^2\cdot\big(3^9\big)^2=\purple{\underline{\big(5\cdot 3^9\big)^2=pp}}$

=========pav38============

$\bf d)~16\cdot100=4^2\cdot10^2= \big(4\cdot10\big)^2=\pink{\underline{40^2}}$

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$\bf e)~4^{15}\cdot121^{17}=\big(2^2\big)^{15}\cdot\big(11^2\big)^{17}=$

$\bf \big(2^{15}\big)^2\cdot\big(11^{17}\big)^2= \red{\underline{\big(2^{15}\cdot11^{17}\big)^2=pp}}$

===========================

$\bf f)~5^{14}\cdot7^8\cdot13^{24}=5^{7\cdot2}\cdot7^{4\cdot2}\cdot13^{12\cdot2}=$

$\bf \big(5^7\big)^2\cdot\big(7^4\big)^2\cdot\big(13^{12}\big)^2= \blue{\underline{\big(5^7\cdot7^4\cdot13^{12}\big)^2 = pp}}$

=========pav38============

$\bf g)~3^{25}+3^{24}=3^{24}\cdot\big(3^{25-24}+3^{24-24}\big)=$

$\bf 3^{24}\cdot\big(3^{1}+3^{0}\big)=3^{24}\cdot\big(3+1\big)=$

$\bf 3^{24}\cdot4=\big(3^{17}\big)^2\cdot2^2=\purple{\underline{\big(3^{17}\cdot2\big)^2=pp}}$  

=========================

$\bf f)~2^{25}-7\cdot2^{20}=2^{20}\cdot\big(2^{25-20}-7\cdot 2^{20-20}\big)=$

$\bf 2^{20}\cdot\big(2^{5}-7\cdot 2^{0}\big)=2^{20}\cdot\big(32-7\big)=$

$\bf 2^{20}\cdot25=2^{20}\cdot 5^{2} =\red{\underline{\big(2^{10}\cdot 5\big)^2=pp}}$

$==pav38==$