Question

B0eecraze (4.6-4.8): 4.6.1) 15. 2.27 - 12) - 75: 2,73-23-3-6-12) - 143 1303-5 - )-5-303) - 15:49 15,5 - 472) - 12 - -5) - 7.5 4.7.1) (x + 5)(x+ 2 () 303-6-23 4)45-755 4.5.10 113-331-30-3: 2) チールラーハット 3003-26-5-23 4)16-07-6-11​

Answer 1

4.6

1)

$\sqrt{3} \times (2 \sqrt{27} - \sqrt{12} ) - \sqrt{75} = \sqrt{3} (2 \sqrt{9 \times 3} - \sqrt{4 \times 3} ) - \sqrt{25 \times 3} = \sqrt{3} \times (2 \times \sqrt{9} \times \sqrt{3} - \sqrt{4} \times \sqrt{3} ) - \sqrt{25} \times \sqrt{3} = \sqrt{3} (2 \times 3 \times \sqrt{3} \times \sqrt{3} ) - 5 \sqrt{3} = \sqrt{3} (6 \times {( \sqrt{3} )}^{2} ) - 5 \sqrt{3} = \sqrt{3} (6 \times 3) - 5 \sqrt{3} = 18 \sqrt{3} - 5 \sqrt{3} = 13 \sqrt{3}$

2)

$\sqrt{75} - 2 \sqrt{3} \times (3 - 6 \sqrt{12} ) + 14 = \sqrt{25 \times 3} - 2 \sqrt{3} \times (3 - 6 \sqrt{4 \times 3} ) + 14 = 5 \sqrt{3} - 2 \sqrt{3} \times (3 - 12 \sqrt{3} ) + 14 = 5 \sqrt{3} - 6 \sqrt{3} + 72 + 14 = - \sqrt{3} + 86 = 86 - \sqrt{3}$

3)

$(3 \sqrt{5} - \sqrt{8} ) \times ( \sqrt{8} + 3 \sqrt{5} ) + \sqrt{48} = (3 \sqrt{5} - \sqrt{8} ) \times (3 \sqrt{5} + \sqrt{8} ) + \sqrt{16 \times 3} = {(3 \sqrt{5} )}^{2} - {( \sqrt{8} )}^{2} - \sqrt{16} \times \sqrt{3} = (9 \times 5) - 8 - 4 \times \sqrt{3} = 45 - 8 - 4 \sqrt{3} = 37 - 4 \sqrt{3}$

4)

$(5 \sqrt{5} - \sqrt{12} ) \times (2 - \sqrt{5} ) + 7 \sqrt{3} = (5 \sqrt{5} - \sqrt{4 \times 3} ) \times (2 - \sqrt{5} ) + 7 \sqrt{3} = (5 \sqrt{5} - 2 \sqrt{3} ) \times (2 - \sqrt{5} ) + 7 \sqrt{3} = 5 \sqrt{5} \times 2 - 5 \sqrt{5} \times \sqrt{5} - 2 \sqrt{3} \times 2 + 2 \sqrt{3} \times \sqrt{5} + 7 \sqrt{3} = 10 \sqrt{5} - 25 - 4 \sqrt{3} + 2 \sqrt{15} + 7 \sqrt{3} = 10 \sqrt{5} + 2 \sqrt{15} + 3 \sqrt{3} - 25$

4.7

1)

$(x + \sqrt{y} )(x + \sqrt{y} ) = {(x + \sqrt{y} )}^{2} = {x}^{2} + 2x \sqrt{y} + {( \sqrt{y} )}^{2} = {x}^{2} + 2x \sqrt{y} + y$

2)

${( \sqrt{x} + \sqrt{xy} )}^{2} = {( \sqrt{x} )}^{2} + 2 \sqrt{x} \sqrt{xy} + {( \sqrt{xy} )}^{2} = x + 2 \sqrt{ {x}^{2} y} + xy = x + 2x \sqrt{y} + xy$

3)

${ (3 \sqrt{6} - 2 \sqrt{3} )}^{2} = {(3 \sqrt{6} )}^{2} - 2 \times 3 \sqrt{6} \times 2 \sqrt{3} + {(2 \sqrt{3} )}^{2} = (9 \times 6) -12 \sqrt{6 \times 3} + (4 \times 3) = 54 - 12 \sqrt{18} + 12 = 66 - 12 \sqrt{9 \times 2} = 66 - 12 \times 3 \times \sqrt{2} = 66 - 36 \sqrt{2}$

4)

${ (4 \sqrt{5} - 7 \sqrt{5} )}^{2} = {(4 \sqrt{5} )}^{2} - 2 \times 4 \sqrt{5} \times 7 \sqrt{5} + {(7 \sqrt{5} )}^{2} = (16 \times 5) - 56 \sqrt{5 \times 5} + (49 \times 5) = 80 - 56 \sqrt{25} + 245 = 325 - 56 \times 5 = 325 - 280 = 45$

4.8

1)

${( \sqrt{15} + 3 \sqrt{5} )}^{2} - 30 \sqrt{3} = {( \sqrt{15} )}^{2} + 2 \times \sqrt{15} \times 3 \sqrt{5} + {(3 \sqrt{5} )}^{2} - 30 \sqrt{3} = 15 + 6 \sqrt{15 \times 5} + (9 \times 5) - 30 \sqrt{3} = 15 + 6 \sqrt{25 \times 3} + 45 - 30 \sqrt{3} = 60 + 6 \times 5 \times \sqrt{3} - 30 \sqrt{3} = 60 + 30 \sqrt{3 } - 30 \sqrt{3} = 60$

2)

${( \sqrt{4 - \sqrt{7} } + \sqrt{ \sqrt{7} + 4 } )}^{2} = {( \sqrt{4 - \sqrt{7} } + \sqrt{ 4 + \sqrt{7} } )}^{2} = {( \sqrt{4 - \sqrt{7} } )}^{2} + 2 \times \sqrt{4 - \sqrt{7} } \times \sqrt{4 + \sqrt{7} } + {( \sqrt{ 4 + \sqrt{7} } )}^{2} = (4 - \sqrt{7} ) + 2 \sqrt{(4 - \sqrt{7})(4 + \sqrt{7} ) } + (4 + \sqrt{7} ) = 16 + 2 \sqrt{ {4}^{2} - {( \sqrt{7} )}^{2} } = 16 + 2 \sqrt{16 - 7} = 16 + 2 \sqrt{9} = 16 + 2 \times 3 = 16 + 6 = 22$

3)

${( \sqrt{5 - 2 \sqrt{6} } + \sqrt{5 + 2 \sqrt{6} } )}^{2} = {( \sqrt{5 - 2 \sqrt{6} } )}^{2} + 2 \times \sqrt{5 - 2 \sqrt{6} } \times \sqrt{5 + 2 \sqrt{6} } + {( \sqrt{5 + 2 \sqrt{6} } )}^{2} = (5 - 2 \sqrt{6} ) + 2 \sqrt{(5 - 2 \sqrt{6})(5 + 2 \sqrt{6} )} + (5 + 2 \sqrt{6} ) = 25 + 2 \sqrt{ {5}^{2} - {(2 \sqrt{6} )}^{2} } = 25 + \sqrt{25 - (4 \times 6)} = 25 + \sqrt{25 - 24} = 25 + \sqrt{1} = 25 + 1 = 26$

4)

${( \sqrt{6 + \sqrt{11} } - \sqrt{6 - \sqrt{11} } )}^{2} = {( \sqrt{6 + \sqrt{11} } )}^{2} - 2 \times \sqrt{6 + \sqrt{11} } \times \sqrt{6 - \sqrt{11} } + {( \sqrt{6 - \sqrt{11} } )}^{2} = (6 + \sqrt{11} ) - 2 \sqrt{(6 + \sqrt{11} )(6 - \sqrt{11}) } + (6 - \sqrt{11} ) = 12 - 2 \sqrt{ {6}^{2} - {( \sqrt{11} )}^{2} } = 12 - 2 \sqrt{36 - 11} = 12 - 2 \sqrt{25} = 12 - 2 \times 5 = 12 - 10 = 2$