Question

Помагите решить умоляю пж

Answer 1

Упростите выражения:

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

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

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

Выполните умножение:

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

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

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

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

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

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

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

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

Упростите выражение:

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

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

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

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