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![1:\
a) sqrt{5} * sqrt{45} = sqrt{5 * 45} = sqrt{5 * 5 * 9} = 5 * 3 = 15\
b) sqrt{562^{2} - 462^{2}} = sqrt{(562 - 462) * (562 + 462)} = sqrt{100 * 1024} = \
= sqrt{10^{2} * 2^{10}} = 10 * 2^{5} = 32 * 10 = 320\
2: \
a) (4 - sqrt{3})(4 + sqrt{3}) = 16 - 3 = 13\
b) (1 + sqrt{5})^{2} - sqrt{20} = 1 + 2sqrt{5} + 5 - sqrt{20} = 6 + sqrt{20} - sqrt{20} = 6\
v) (2 + sqrt{9x})(2 - 3sqrt{x}) = (2 + sqrt{9x})(2 - sqrt{9x}) = 4-9x\](https://tex.z-dn.net/?f=1%3A%5C%0Aa%29++sqrt%7B5%7D+%2A+sqrt%7B45%7D+%3D+sqrt%7B5+%2A+45%7D+%3D+sqrt%7B5+%2A+5+%2A+9%7D+%3D+5+%2A+3+%3D+15%5C%0Ab%29+sqrt%7B562%5E%7B2%7D+-+462%5E%7B2%7D%7D+%3D+sqrt%7B%28562+-+462%29+%2A+%28562+%2B+462%29%7D+%3D+sqrt%7B100+%2A+1024%7D+%3D+%5C%0A%3D+sqrt%7B10%5E%7B2%7D+%2A+2%5E%7B10%7D%7D+%3D+10+%2A+2%5E%7B5%7D+%3D+32+%2A+10+%3D+320%5C%0A2%3A+%5C%0Aa%29+%284+-+sqrt%7B3%7D%29%284+%2B+sqrt%7B3%7D%29+%3D+16+-+3+%3D+13%5C%0Ab%29+%281+%2B+sqrt%7B5%7D%29%5E%7B2%7D+-+sqrt%7B20%7D+%3D+1+%2B+2sqrt%7B5%7D+%2B+5+-+sqrt%7B20%7D+%3D+6+%2B+sqrt%7B20%7D+-+sqrt%7B20%7D+%3D+6%5C%0Av%29+%282+%2B+sqrt%7B9x%7D%29%282+-+3sqrt%7Bx%7D%29+%3D+%282+%2B+sqrt%7B9x%7D%29%282+-+sqrt%7B9x%7D%29+%3D+4-9x%5C%0A "1:\
a) sqrt{5} * sqrt{45} = sqrt{5 * 45} = sqrt{5 * 5 * 9} = 5 * 3 = 15\
b) sqrt{562^{2} - 462^{2}} = sqrt{(562 - 462) * (562 + 462)} = sqrt{100 * 1024} = \
= sqrt{10^{2} * 2^{10}} = 10 * 2^{5} = 32 * 10 = 320\
2: \
a) (4 - sqrt{3})(4 + sqrt{3}) = 16 - 3 = 13\
b) (1 + sqrt{5})^{2} - sqrt{20} = 1 + 2sqrt{5} + 5 - sqrt{20} = 6 + sqrt{20} - sqrt{20} = 6\
v) (2 + sqrt{9x})(2 - 3sqrt{x}) = (2 + sqrt{9x})(2 - sqrt{9x}) = 4-9x\")
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(a+Va):(Va+1) = (Va*Va+Va):(Va+1) = Va*(Va+1):(Va+1) = Va
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