Question

5. Adu la forma cea mai simplă:
a) 2V27 +4V12-3V75 =
b) (5V5+V45)×V5=
c) (V18-V6) : V2= ​

Answer 1

a)

$2 \sqrt{27} = 2 \sqrt{3 \times 3 \times 3} = 2 \times 3 \sqrt{3} = \\ = 6 \sqrt{3}$

$4 \sqrt{12} = 4 \sqrt{3 \times 2 \times 2} = 4 \times 2 \sqrt{3} = \\ = 8 \sqrt{3}$

$3 \sqrt{75} = 3 \sqrt{5 \times 5 \times 3} = 3 \times 5 \sqrt{3} = \\ = 15 \sqrt{3}$

$2 \sqrt{27} + 4 \sqrt{12} - 3 \sqrt{75} = \\ = 8 \sqrt{3} + 15 \sqrt{3} - 5 \sqrt{3} = \\ = 18 \sqrt{3}$

b)

$(5 \sqrt{5} + \sqrt{45} ) \sqrt{5} = \\ = (5 \sqrt{5 } + \sqrt{3 \times 3 \times 5} ) \times \sqrt{5} = \\ = (5 \sqrt{5} + 3 \sqrt{5} ) \times \sqrt{5} = \\ = 5 \sqrt{5 \times 5} + 3 \sqrt{5 \times 5} = \\ = 5 \times 5 + 3 \times 5 = \\ = 25 \times 15 = 40$

c)

$( \sqrt{18} - \sqrt{6} ) \div \sqrt{2} = \\ = \sqrt{18 \div 2} - \sqrt{6 \div 2} = \\ = \sqrt{9} - \sqrt{3} = \\ = \sqrt{3 \times 3} - \sqrt{3} = \\ = 3 - \sqrt{3}$

Answer 2

$\it a)\ \ =6\sqrt3+8\sqrt3-15\sqrt3=-\sqrt3$

$\it b)\ \ =(5\sqrt5+3\sqrt5)\cdot\sqrt5=8\sqrt5\cdot\sqrt5=8\cdot5=40$