Question

aratati ca numarul a=2(1+2+3....224)+225 este patrat perfect si calculati radical din a

Answer 1

Răspuns:

a=2(1+2+3....224)+225

a=2·[224·(224+1)]/2+225

a=50400+225

a=50625

a=225² → p.p

√a=225

Answer 2

Răspuns: Ai mai jos demonstrația

Explicație pas cu pas:

$\bf a=2\cdot (1+2+3....224)+225$

$\bf a=2\cdot \big[(1+224)\cdot 224 : 2\big]+225$

$\bf a=2\cdot \big(225\cdot 224 : 2\big)+225$

$\bf a=2\cdot \big(225\cdot 112\big)+225$

$\bf a=2\cdot 25200+225$

$\bf a=50400+225$

$\bf a=50625$

$\red{\boxed{\bf a=225^{2} \implies ~patrat ~perfect}}$

$\bf \sqrt{a}=\sqrt{225^{2}} \implies \purple{\boxed{\bf a = 225}}$

$==pav38==$