Question

Calcule as radiciações abaixo:
1) √75- 2√12 + √27=4√3

2)√12 - 9√3 + √75=

3)√98 - √18 - 5√32=

4)5√180 + √245 - 17√5=

Answer 1

Resposta:

$1)\\ \sqrt{75} -2\sqrt{12} +\sqrt{27} =\\ \\ \sqrt{3.5^2} -2\sqrt{2^2.3} +\sqrt{3^2.3} =\\ \\ 5\sqrt{3} -4\sqrt{3} +3\sqrt{3} =\\ \\ 8\sqrt{3} -4\sqrt{3} =4\sqrt{3} \\ \\ 2)\\ \sqrt{12} -9\sqrt{3} +\sqrt{75} =\\ \\ \sqrt{2.3^2} -9\sqrt{3} +\sqrt{3.5^2} =\\ \\ 3\sqrt{2} -9\sqrt{3} +5\sqrt{3} =\\ \\ 8\sqrt{3} -9\sqrt{3} =-\sqrt{3}$

$3)\\ \sqrt{98} -\sqrt{18} -5\sqrt{32} =\\ \\ \sqrt{2.7^2} -\sqrt{2.3^2} -5\sqrt{2^2.2^2.2} =\\ \\ 7\sqrt{2} -3\sqrt{2} -5.2.2\sqrt{2} =\\ \\ 7\sqrt{2} -3\sqrt{2} -20\sqrt{2} =\\ \\ 7\sqrt{2} -23\sqrt{2} =-16\sqrt{2} \\ \\ 4)\\ \sqrt{180} +\sqrt{245} -17\sqrt{5} =\\ \\ \sqrt{2^2.3^2.5} +\sqrt{5.7^2} -17\sqrt{5} =\\ \\ 6\sqrt{5} +7\sqrt{5} -17\sqrt{5} \\ \\ 13\sqrt{5} -17\sqrt{5} =-4\sqrt{5}$