Question

Упростите выражение:

1) 3√5 * √15 ,  2) frac{6}{√3} ,3) frac{√48}{√3} ,  4)  frac{8√32}{2√72}

Answer 1

1) 15√3

2) 2√3

3) √16=4

4) 4√(1/2)

Answer 2

$3sqrt{5}*sqrt{15}=3sqrt{5}*sqrt{3*5}=3*sqrt{3}*sqrt{5}*sqrt{5}=3*5*sqrt{3}=15sqrt{3}$

 

$frac{6}{sqrt{3}}=frac{2*3}{sqrt{3}}=frac{2*sqrt{3}*sqrt{3}}{sqrt{3}}=2sqrt{3}$

 

$frac{sqrt{48}}{sqrt{3}}=sqrt{frac{48}{3}}=sqrt{16}=sqrt{4^2}=4$

 

$frac{8sqrt{32}}{2sqrt{72}}=frac{2*4*sqrt{16*2}}{2*sqrt{36*2}}=frac{4sqrt{16}*sqrt{2}}{sqrt{36}*sqrt{2}}=frac{4*sqrt{4^2}}{sqrt{6^2}}=frac{4*4}{6}=frac{8}{3}$