Explicație pas cu pas:
a)
[tex]\Big( \sqrt{450} - \sqrt{200}\Big) - \Big( \sqrt{1250} - \sqrt{1800}\Big) = \Big( \sqrt{2 \cdot {3}^{2} \cdot {5}^{2} } - \sqrt{ {2}^{3} \cdot {5}^{2} }\Big) - \Big( \sqrt{2 \cdot {5}^{4} } - \sqrt{ {2}^{3} \cdot {3}^{2} \cdot {5}^{2} }\Big) = 15 \sqrt{2} - 10 \sqrt{2} - 25 \sqrt{2} + 30 \sqrt{2} = \bf 10 \sqrt{2} [/tex]
b)
[tex]\sqrt{1805} - \Big( \sqrt{1620} - \sqrt{845} \Big) - \sqrt{720} = \sqrt{5 \cdot {19}^{2} } - \sqrt{ {2}^{2} \cdot {3}^{4} \cdot 5} + \sqrt{5 \cdot {13}^{2} } - \sqrt{ {2}^{4} \cdot {3}^{2} \cdot 5} = 19 \sqrt{5} - 18 \sqrt{5} + 13 \sqrt{5} - 12 \sqrt{5} = \bf 2\sqrt{5}[/tex]
c)
[tex]\sqrt{160} - \Big( \sqrt{810} - \sqrt{9610} + \sqrt{6760} \Big) = \sqrt{ {2}^{5} \cdot 5} - \sqrt{2 \cdot {3}^{4} \cdot 5} + \sqrt{2 \cdot 5 \cdot {31}^{2} } - \sqrt{ {2}^{3} \cdot 5 \cdot {13}^{2} } = 4 \sqrt{10} - 9 \sqrt{10} + 31 \sqrt{10} - 26 \sqrt{10} = \bf 0[/tex]
d)
[tex]\sqrt{4375} - \Big( \sqrt{3087} + \sqrt{4732} - \sqrt{2268}\Big) = \sqrt{ {5}^{4} \cdot 7} - \sqrt{ {3}^{2} \cdot {7}^{3}} - \sqrt{ {2}^{2} \cdot 7 \cdot {13}^{2} } + \sqrt{ {2}^{2} \cdot {3}^{4} \cdot 7} = 25 \sqrt{7} - 21 \sqrt{7} - 26 \sqrt{7} + 18 \sqrt{7} = \bf - 4 \sqrt{7}[/tex]
