Question

Сделайте пж даю 100 баллов!!!!.!!..!!!!!!.!!.!!

Answer 1

Ответ:

1.

$\sqrt{50} + \sqrt{98} - \sqrt{200} = \\ = \sqrt{25 \times 2} + \sqrt{49 \times 2} - \sqrt{100 \times 2} = \\ = 5 \sqrt{2} + 7 \sqrt{2} - 10 \sqrt{2} = 2 \sqrt{2}$

2.

$5 \sqrt{12} - 2 \sqrt{48} + 2 \sqrt{27} = \\ = 5 \sqrt{4 \times 3} - 2 \sqrt{16 \times 3} + 2 \sqrt{9 \times 3} = \\ = 5 \times 2 \sqrt{3} - 2 \times 4 \sqrt{3} + 2 \times 3 \sqrt{3} = \\ = 10 \sqrt{3} - 8 \sqrt{3} + 6 \sqrt{3} = 8 \sqrt{3}$

3.

$\sqrt{20} + 2 \sqrt{45} - 3 \sqrt{500} = \\ = \sqrt{4 \times 5} + 2 \sqrt{9 \times 5} - 3 \sqrt{100 \times 5} = \\ = 2 \sqrt{5} + 6 \sqrt{5} - 30 \sqrt{5} = \\ = - 22 \sqrt{5}$

4.

$\sqrt{9a} + \sqrt{25a} - \sqrt{36a} = \\ = 3 \sqrt{a} + 5 \sqrt{a} - 6 \sqrt{a} = 2 \sqrt{a}$

5.

$5 \sqrt{27t} - 4 \sqrt{48t} - 2 \sqrt{12t} = \\ = 5 \times 3 \sqrt{3 t} - 4 \times 4 \sqrt{3t} - 2 \times 2 \sqrt{3 t } = \\ = 15 \sqrt{3t} - 16 \sqrt{3t} - 4 \sqrt{3t} = - 5 \sqrt{3t}$

__________________

$\frac{2}{ \sqrt{5} - \sqrt{3} } \times \frac{ \sqrt{5} + \sqrt{3} }{ \sqrt{5} + \sqrt{3} } = \\ = \frac{2( \sqrt{5} + \sqrt{3} )}{ {( \sqrt{5}) }^{2} - {( \sqrt{3}) }^{2} } = \frac{2( \sqrt{5} + \sqrt{3} )}{5 - 3} = \\ = \frac{2( \sqrt{5} + \sqrt{3}) }{2} = \sqrt{5} + \sqrt{3}$

$\frac{ \sqrt{a} }{ \sqrt{a} + \sqrt{b} } \times \frac{ \sqrt{a} - \sqrt{b} }{ \sqrt{a} - \sqrt{b} } = \\ = \frac{ \sqrt{a} ( \sqrt{a} - \sqrt{b} ) }{a - b} = \frac{a - \sqrt{ab} }{a - b}$

$\frac{1}{a + \sqrt{b} } \times \frac{ a- \sqrt{b} }{ a- \sqrt{b} } = \frac{a - \sqrt{b} }{ {a}^{2} - b}$

$\frac{8}{ \sqrt{6} - x} \times \frac{ \sqrt{6} + x}{ \sqrt{6} + x} = \frac{8( \sqrt{6} + x)}{6 - {x}^{2} }$