Question

Rezultatul calculului √48-(16 supra √32 - 18 supra √243) ·√6= VA ROG AM NEVOIE URGEENT

Answer 1

Răspuns:

Explicație pas cu pas:

√48=√16×3=4√3

√32=√2^5=4√2

√243=√3^5=9√3

4√3-(16/4√2-18/9√3)·√6=4√3-(4√2/2-2√3/3)√6=

=4√3-(2√2-2√3/3)√6=4√3-4√3+2√2=

=2√2

Answer 2

Descompunem in factori primi numerele de sub radical pentru a ne fi mai usor la calcule

48 = 2⁴·3 => √48 = 4√3

32 = 2⁵ => √32 = 4√2

243 = 3⁵ => √243 = 9√3

$\bf \sqrt{48} -\Big(\dfrac{16}{\sqrt{32}} -\dfrac{18}{\sqrt{243}}\Big)\cdot\sqrt{6} =$

$\bf 4\sqrt{3} -\Big(\dfrac{16}{4\sqrt{2}} -\dfrac{18}{9\sqrt{3}}\Big)\cdot\sqrt{6} =$

$\bf 4\sqrt{3} -\Big(\dfrac{\not16}{\not4\sqrt{2}} -\dfrac{\not18}{\not9\sqrt{3}}\Big)\cdot\sqrt{6} =$

$\bf 4\sqrt{3} -\Big(\dfrac{4}{\sqrt{2}} -\dfrac{2}{\sqrt{3}}\Big)\cdot\sqrt{6} =$

$\bf 4\sqrt{3} -\Big(\dfrac{4\cdot\sqrt{2} }{\sqrt{2}\cdot\sqrt{2} } -\dfrac{2\cdot\sqrt{3} }{\sqrt{3}\cdot\sqrt{3} }}\Big)\cdot\sqrt{6} =$

$\bf 4\sqrt{3} -\Big(\dfrac{4\cdot\sqrt{2} }{2} -\dfrac{2\cdot\sqrt{3} }{3}}\Big)\cdot\sqrt{6} =$

$\bf 4\sqrt{3} -\Big(\dfrac{\not4\cdot\sqrt{\not2}}{2} -\dfrac{2\cdot\sqrt{3} }{3}}\Big)\cdot\sqrt{6} =$

$\bf 4\sqrt{3} -\Big(2\sqrt{2} -\dfrac{2\cdot\sqrt{3} }{3}}\Big)\cdot\sqrt{6} =$

$\bf 4\sqrt{3} -\Big(2\sqrt{12} -\dfrac{2\cdot\sqrt{18} }{3}}\Big)=$

$\bf 4\sqrt{3} -\Big(4\sqrt{3} -\dfrac{6\cdot\sqrt{2} }{3}}\Big)=$

$\bf 4\sqrt{3} -\Big(4\sqrt{3} -\dfrac{\not6\cdot\sqrt{2} }{\not3}}\Big)=$

$\bf 4\sqrt{3} -(4\sqrt{3} -2\sqrt{2})=$

$\bf 4\sqrt{3} -4\sqrt{3} +2\sqrt{2}=$

$\bf \not4\sqrt{3} -\not4\sqrt{3} +2\sqrt{2}=$

$\boxed{\bf 2\sqrt{2}}$

PS: 1) Am incercat sa iti scriu toate calculele ca sa intelegi, daca ai intrebari imi scrii in comentarii

    2) Am atasat si o fotografie in caz de telefonul tau nu citeste scrisul matematic

         ≈≈≈≈ Mult succes! ≈≈≈≈