Question

1. Scoateţi factorii de sub radical:
a) √96; √48; √72;√56; √108; √162;√192;√150;
b) √√216;√329; √180; √147;√√252;√√448;√√405;√√242;
c) √567;√√363; √294;√√360;√√540;√√288;√338;√432;d
d) √507; √810; √588;√√980;√175;√√112;√√450;√768.

Answer 1

Explicație pas cu pas:

a)

√96 = √(2⁵×3¹) = 2²√(2×3) = 4√6

√48 = √(2⁴×3¹) = 2²√3 = 4√3

√72 = √(2³×3²) = 2×3√2 = 6√2

√56 = √(2³×7) = 2×√(2×7) = 2√14

√108 = √(2²×3³) = 2×3√3 = 6√3

√162 = √(2¹×3⁴) = 3²√2 = 9√2

√192 = √(2⁶×3¹) = 2³√3 = 8√3

√150 = √(2¹×3¹×5²) = 5√(2×3) = 5√6

Answer 2

$\it\sqrt{96}=\sqrt{16\cdot6}=4\sqrt6\\ \\ \sqrt{48}=\sqrt{16\cdot3}=4\sqrt3\\ \\\sqrt{72}=\sqrt{36\cdot2}=6\sqrt2\\ \\ \sqrt{56}=\sqrt{4\cdot14}=2\sqrt{14}\\ \\\sqrt{108}=\sqrt{36\cdot3}=6\sqrt3\\ \\ \sqrt{162}=\sqrt{81\cdot2}=9\sqrt2\\ \\ \sqrt{192}=\sqrt{64\cdot3}=8\sqrt3\\ \\ \sqrt{150}=\sqrt{25\cdot6}=5\sqrt6$