Question

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Answer 1

Salutare

Folosim proprietatile radicalilor adica :

$\sqrt{(a)*b)} = \sqrt(a)*\sqrt(b)\\\\\sqrt(a/b) =\sqrt(a)/\sqrt(b)$

Si vom da si factor comun.

a)$2*\sqrt{2}*\sqrt{5} -3*\sqrt{5} *\sqrt{2} +4*\sqrt{5} *3*\sqrt{2} -5*\sqrt{5} *4*\sqrt{2}$

Dam factor comun pe $\sqrt{2}*\sqrt{5}$ si rezulta :

$\sqrt{2} *\sqrt{5} * (2-3+4*3-5*4)\\\sqrt{10} *(-1+12-20)\\\sqrt{10}*(11-20)\\\sqrt{10}*(-9)\\-9*\sqrt{10}$

b)$\frac{\sqrt{21} }{\sqrt{7} } -5*\frac{\sqrt{15} }{\sqrt{5} } +2*3*\sqrt{3} -4*\frac{\sqrt{30} }{\sqrt{10} } \\\\\sqrt{3} -5*\sqrt{3} +6*\sqrt{3} -4*\sqrt{3}$

Dam factor comun pe $\sqrt{3}$ si rezulta :

$\sqrt{3}*(1-5+2*3-4)\\\\\sqrt{3}*(1-5+6-4)\\\\\sqrt{3}*(-2)\\\\-2*\sqrt{3}$