Question

Помагите решить умоляю пж

Answer 1

Упростите выражения:

1) $\sqrt{25a} + \sqrt{36a} + \sqrt{49a} = 5\sqrt{a} + 6\sqrt{a} + 7\sqrt{a} = 18\sqrt{a}$

2) $\sqrt{27} - \sqrt{12} + \sqrt{300} = \sqrt{3^{2}*3} - \sqrt{2^{2}*3} + \sqrt{10^{2}*3} = 3\sqrt{3} - 2\sqrt{3} + 10\sqrt{3} = 11\sqrt{3}$

3) $3\sqrt{32a} - 5\sqrt{98a} + \frac{1}{3}\sqrt{288a} = 3\sqrt{4^{2}*2a} - 5\sqrt{7^{2}*2a} + \frac{1}{3}\sqrt{12^{2}*2a} = 12\sqrt{2a} - 35\sqrt{2a} + 4\sqrt{2a} = -19\sqrt{2a}$

Выполните умножение:

1) $(\sqrt{63} - \sqrt{28})*\sqrt{7} = \sqrt{7*9*7} - \sqrt{7*4*7} = 7*3 - 7*2 = 7$

2) $(7\sqrt{3} + \sqrt{48} - \sqrt{75})*\sqrt{3} = 7\sqrt{3*3} + \sqrt{16*3*3} - \sqrt{25*3*3} = 7*3 + 4*3 - 5*3 = 21 + 12 - 15 = 18$

3) $(6 - \sqrt{5})(2 + 7\sqrt{5}) = 6*2 + 6*7\sqrt{5} - 2\sqrt{5} - 7\sqrt{5*5} = 12 + 42\sqrt{5} - 2\sqrt{5} - 35 = 40\sqrt{5} - 23$

4) $(5\sqrt{2} + 6\sqrt{3})(6\sqrt{2} - 5\sqrt{3}) = 5 * 6\sqrt{2*2} - 5*5\sqrt{2*3} + 6*6\sqrt{3*2} - 6*5\sqrt{3*3} = 5*6*2 - 5*5\sqrt{6} + 6*6\sqrt{6} - 6*5*3 = 60 - 25\sqrt{6} + 36\sqrt{6} - 90 = 11\sqrt{6} - 30$

5) $(\sqrt{17} - \sqrt{11})(\sqrt{17} + \sqrt{11}) = 17 - 11 = 6$

6) $(2\sqrt{x} - 5\sqrt{y})(2\sqrt{x} + 5\sqrt{y}) = 4x - 25y$

7) $(\sqrt{6} - 2)^{2} = (\sqrt{6})^{2} - 2*\sqrt{6}*2 + 2^{2} = 6 - 4\sqrt{6} + 4 = 10 - 4\sqrt{6}$

8) $(3\sqrt{7} - 2\sqrt{3})^{2} = (3\sqrt{7})^{2} - 2*3\sqrt{7}*2\sqrt{3} + (2\sqrt{3})^{2} = 9*7 - 12\sqrt{21} + 4*3 = 63 - 12\sqrt{21} + 12 = 75 - 12\sqrt{21}$

Упростите выражение:

1) $(2\sqrt{3} + 6\sqrt{20} - 7\sqrt{45})*\sqrt{5} - \sqrt{60} = 2\sqrt{3*5} + 6\sqrt{20*5} - 7\sqrt{9*5*5} - \sqrt{60} = 2\sqrt{15} + 6*10 - 7*3*5 - 2\sqrt{15} = 60 - 105 = -45$

2) $(\sqrt{7} - 2\sqrt{3})(2\sqrt{3} + \sqrt{7}) - (\sqrt{6} - 3\sqrt{2})^{2} = 7 - 4*3 - (6 - 2*3\sqrt{12} + 9*2) = 7 - 12 - 6 + 12\sqrt{3} - 18 = 12\sqrt{3} - 19$

3) $(5 - \sqrt{2})^{2} + (3 + \sqrt{2})^{2} = 25 - 10\sqrt{2} + 2 + 9 + 6\sqrt{2} + 2 = 36 - 10\sqrt{2}$

4) $(\sqrt{9 - 4\sqrt{5}} - \sqrt{9 + 4\sqrt{5}})^{2} = 9 - 4\sqrt{5} - 2\sqrt{9 - 4\sqrt{5}}*\sqrt{9 + 4\sqrt{5}} + 9 + 4\sqrt{5} = 18 - 2\sqrt{(9 - 4\sqrt{5})(9 + 4\sqrt{5})} = 18 - 2\sqrt{81 - 16*5} = 18 - 2\sqrt{81 - 80} = 18 - 2\sqrt{1} = 18 - 2 = 16$