Question

11) Упростите выражения. a) √75 +√48-√300 c) √16n+√25n - √9n b) 3√8 - √50 + 28 d) √3а - 2√12а +375​

Answer 1

$a) \: \: \: \: \: \sqrt{75} + \sqrt{48} - \sqrt{300} = \sqrt{25 \times 3} + \sqrt{16 \times 3} - \sqrt{100 \times 3} = 5 \sqrt{3} + 4 \sqrt{3} - 10 \sqrt{3} = 9 \sqrt{3} - 10 \sqrt{3} = - \sqrt{3}$

$c) \: \: \: \: \: \sqrt{16n} + \sqrt{25n} - \sqrt{9n} = 4 \sqrt{n} + 5 \sqrt{n} - 3 \sqrt{n} = 9 \sqrt{n} - 3 \sqrt{n} = 6 \sqrt{n} = \sqrt{36n}$

$b) \: \: \: \: \: 3 \sqrt{8} - \sqrt{50} + 28 = 3 \sqrt{2 \times 4} - \sqrt{25 \times 2} + 28 = 6 \sqrt{2} - 5 \sqrt{2} + 28 = \sqrt{2} + 28 = 29 \sqrt{2}$

$d) \: \: \: \: \: \sqrt{3a} - 2 \sqrt{12a} + 375 = \sqrt{3a} - 2 \sqrt{3 \times 4a} + 375 = \sqrt{3a} - 4 \sqrt{3a} + 375 = - 3 \sqrt{3a} + 375 = 372 \sqrt{3a}$