Question

SCOATEȚI FACTORII DE SUB RADICAL ȘI CALCULAȚI: a) 2√50 + 3√18
b) √12 -√27;
c) 5√20 - 9√45
d) 3√150 + √54 + 2√36
e)-2 √48 - 5√75-√108​

Answer 1

Răspuns:

a)

$= 2 \sqrt{25 \times 2} + 3 \sqrt{9 \times 2} = 2 \sqrt{25} \sqrt{2} + 3 \sqrt{9} \sqrt{2} = 2 \times 5 \times \sqrt{2} + 3 \times 2 \times \sqrt{2 } = 10 \sqrt{2} + 6 \sqrt{2} = 16 \sqrt{2}$

b)

$= 5 \sqrt{4 \times 5} - 9 \sqrt{9 \times 5} = 5 \sqrt{4} \sqrt{5} - 9 \sqrt{9} \sqrt{5} = 5 \times 2 \times \sqrt{5} - 9 \times 3 \times \sqrt{5} = 10 \sqrt{5} - 27 \sqrt{5} = - 17 \sqrt{5}$

c)

$= 3 \sqrt{25 \times 6} + \sqrt{9 \times 6} + 2 \times 6 = 3 \sqrt{25 } \sqrt{6} + \sqrt{9} \sqrt{6} + 12 = 3 \times 5 \times \sqrt{6} + 3 \sqrt{6} + 12 = 15 \sqrt{6} + 3 \sqrt{6} + 12 = 18 \sqrt{6} + 12 = 6(3 \sqrt{6} + 2)$

d)

$= - 2 \sqrt{16 \times 3} - 5 \sqrt{25 \times 3} - \sqrt{36 \times 3} = - 2 \sqrt{16} \sqrt{3} - 5 \sqrt{25} \sqrt{3} - \sqrt{36} \sqrt{3} = - 2 \times 4 \times \sqrt{3} - 5 \times 5 \times \sqrt{3} - 6 \times \sqrt{3} = - 8 \sqrt{3} - 25 \sqrt{3} - 6 \sqrt{3} = - 39 \sqrt{6}$