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八上数学题,半小时内给我√是根号的意思1.比较大小2的平方根与3的立方根2000的平方根与3000的立方根2.计算(1)3√2-½√3+1\3-√2+√3(2)27的立方根+|3-√5|-(√9-8的立方根)²+3√53.
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答案和解析
1.因 2^(1/2)^ 6 = 8 < 3^(1/3)^6= 9
所以 2^(1/2) < 3^(1/3)
2000 ^(1/2) = 4 ^(1/2) 5 ^(1/2) 100^(1/2) = 20 x 5^(1/2)= 10 x 2x 5^(1/2)
3000^ (1/3) = 3^(1/3) 1000^(1/3) = 3^(1/3) x 10
因 2x5^(1/2) > 3^(1/3) 所以 2000 ^(1/2)> 3000^ (1/3)
2.27的立方根+|3-√5|-(√9-8的立方根)²+3√5
= 3 + 3-√5 - (3-2)^2 +3√5
= 3 + 3-√5 - 1 +3√5
= 5+ 2√5
3.①√11-2= 1.3166247903553998491149327366.
②√1111-22=11.3316666249979165364492180663525.
③√111111-222=111.333166666624999979166653645824218...
④√11111111-2222=1111.3333166666666249999997916666653645..
重覆1和3
4.√3
5.-1,0,1,2共4个
6.3倍 (体积之比的是线之比的3次方)
所以 2^(1/2) < 3^(1/3)
2000 ^(1/2) = 4 ^(1/2) 5 ^(1/2) 100^(1/2) = 20 x 5^(1/2)= 10 x 2x 5^(1/2)
3000^ (1/3) = 3^(1/3) 1000^(1/3) = 3^(1/3) x 10
因 2x5^(1/2) > 3^(1/3) 所以 2000 ^(1/2)> 3000^ (1/3)
2.27的立方根+|3-√5|-(√9-8的立方根)²+3√5
= 3 + 3-√5 - (3-2)^2 +3√5
= 3 + 3-√5 - 1 +3√5
= 5+ 2√5
3.①√11-2= 1.3166247903553998491149327366.
②√1111-22=11.3316666249979165364492180663525.
③√111111-222=111.333166666624999979166653645824218...
④√11111111-2222=1111.3333166666666249999997916666653645..
重覆1和3
4.√3
5.-1,0,1,2共4个
6.3倍 (体积之比的是线之比的3次方)
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