Question

Calculati:
18) √6:√6;
19) 7√3×√3;
20) 4√6:√3;
21) -9√14:√7;
22)-√20:√10;
23) 3√7:(-3√7);
24) 8√6:(-3√2);
25) -24√10:(-3√5);
26) 9√7:4√3;
27) 9,6√15:(-2√3);
28) 4,8√12:2,4√6;
29) 2/3√6:3/2√2;
30) 1 intreg si 2/3√10:1 intreg si 1/2√5;
31) (2√3)²+(3√2)²;
32) (2√5)²-(5√2)²;
33) (2√6)²-(3√3)².
Va rog frumos!

Answer 1

18.
$\sqrt{6} \div \sqrt{6} = 1$
19.
$7 \sqrt{3} \times \sqrt{3} = \\ = 7 \times 3 \\ = 21$
20.
$4 \sqrt{6} \div \sqrt{3} = 4\sqrt{2}$
21.
$- 9 \sqrt{14} \div \sqrt{7} = - 9 \sqrt{2}$
22.
$- \sqrt{20} \div \sqrt{10} = - \sqrt{2}$
23.
$3 \sqrt{7} \div ( - 3 \sqrt{7} ) = - 1$
24.
$8 \sqrt{6} \div ( - 3 \sqrt{2} ) = \\ = - \frac{8 \sqrt{6} }{3 \sqrt{2} } \\ = - \frac{8 \sqrt{3} }{3}$
25.
$- 24 \sqrt{10} \div ( - 3 \sqrt{5} ) = 8 \sqrt{2}$
26.
$9 \sqrt{7} \div 4 \sqrt{3} = \\ = \frac{9 \sqrt{7} }{4} \times \sqrt{3} \\ = \frac{9 \sqrt{21} }{4}$
27.
$9.6 \sqrt{15} \div ( - 2 \sqrt{3} ) = \\ = - \frac{48}{5} \times -\frac{ \sqrt{15} }{2 \sqrt{3} } \\ = - \frac{24}{5} \times \sqrt{5} \\ = - \frac{24 \sqrt{5} }{5}$
28.
$4.8 \sqrt{12} \div 2.4 \sqrt{6} = \\ = \frac{24}{5} \times 2 \sqrt{3} \div \frac{12}{5} \times \sqrt{6} \\ = 24 \times 2 \sqrt{3} \times \frac{1}{12} \sqrt{6} \\ = 2 \times 2 \sqrt{3} \sqrt{6} \\ = 4 \sqrt{18} \\ = 12 \sqrt{2}$
29.
$\frac{2}{3} \times \sqrt{6} \div \frac{3}{2} \times \sqrt{2} = \\ = \frac{2}{3} \sqrt{6} \times \frac{2}{3} \sqrt{2} \\ = \frac{4 \sqrt{12} }{9} \\ = \frac{8 \sqrt{3} }{9}$
30.
$\frac{5}{3} \sqrt{10} \div \frac{3}{2} \sqrt{5} = \\ = \frac{5}{3} \sqrt{10} \times \frac{2}{3} \sqrt{5} \\ = \frac{10 \sqrt{50} }{9} \\ = \frac{50 \sqrt{2} }{9}$
31.
$(2 \sqrt{3})^{2} + (3 \sqrt{2})^{2} = \\ (2^{2} \times { \sqrt{3} }^{2} ) + ( {3}^{2} \times { \sqrt{2} }^{2} ) \\ = 4 \times 3 + 9 \times 2 \\ = 30$
32.
$(2 \sqrt{5} )^{2} - ( 5\sqrt{2})^{2} = \\ = 20 - 50 \\ = - 30$
33.
$(2 \sqrt{6} )^{2} - (3 \sqrt{3} )^{2} = \\ 24 - 27 \\ = - 3$