有理數,無理數(數學高手入黎ar)

Question

1a.) 將 √2/√3有理化
1b.) 化簡 3/2 x √6 + √3/√2

2a.)將1/√6有理化
2b.) 化簡4√6/3 - 2/√6

3.)9/√12 - √32/6

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Answer 1

1a.) 將 √2/√3有理化
√2/√3 = (√2*√3)/(√3*√3)
= √6 / 3

1b.) 化簡 3/2 x √6 + √3/√2
= 3√6 / 2 + (√3*√2)/(√2*√2)
= 3√6 / 2 + √6 / 2
= [3√6 + √6] / 2
= 4√6 / 2
= 2√6

2a.)將1/√6有理化
1/√6
= √6 / (√6*√6)
= √6 / 6

2b.) 化簡4√6/3 - 2/√6
4√6/3 - 2/√6
= 4√6/3 – (2√6)/(√6*√6)
= 4√6/3 – 2√6 / 6
= 4√6/3 – √6 / 3
= [4 – 1]√6/ 3
= √6

3.)9/√12 - √32/6
9/√12 - √32/6
=9/√(22x3) - √(42x2)/6
=9/(2√3) - 4√2/6
=9√3/(2√3*√3) - 4√2/6
=9√3/(2*3) - 4√2/6
=9√3/6 - 4√2/6
= (9√3 - 4√2)/6

Answer 2

有理數 (rational number)
無理數 (irrational number)
分母有理化 (rationalization of the denominator)：將分母變成有理數。
有理數是指只要能以分數形式表現出來的數，就是有理數(當然必須限定是分母、分子都是整數，且分母不得為0)。所以整數、有限小數、循環小數、及分數都是有理數。
1a.) 將 √2/√3有理化
=√2/√3
=√2/√3×√3 / √3
=√2‧3 / (√3)2
=√6 / 3

1b.) 化簡 3/2 ×√6 + √3/√2
3/2 ×√6 + √3/√2
=3√6 / 2 + √3 / √2
=3√6‧√2 / 2√2 + 2√3 / 2√2
=3√12 + 2√3 / 2√2
=3√4‧3 + 2√3 / 2√2
=6√3 + 2√3 / 2√2
=8√3 / 2√2
=4√3 / √2
=4√3 /√2×√2 / √2
=4√6 / 2
=2√6

2a.)將1/√6有理化
=1 /√6
=1 /√6×√6 /√6
=√6 / (√6)2
=√6 / 6

2b.) 化簡4√6/3﹣2 /√6
=4√6 / 3﹣2 /√6
=4√6 ‧√6 / 3√6﹣2 (3) / 3√6
=4(6)﹣6 / 3√6
=24﹣6 / 3√6
=18 / 3√6
=18 / 3√6×√6 /√6
=18√6 / 3√6‧√6
=18√6 / 3(6)
=18√6 / 18
=√6

3.)9 /√12﹣√32 / 6
9/√12 - √32/6
=9/√(22x3) - √(42x2)/6
=9/(2√3) - 4√2/6
=9√3/(2√3*√3) - 4√2/6
=9√3/(2*3) - 4√2/6
=9√3/6 - 4√2/6
= (9√3 - 4√2)/6

Answer 3

1a.) √2/√3
= (√2/√3 ) x (√3/√3)
= (√2 x √3)/3
= √6/3
1b.) 3/2 x √6 + √3/√2
= 3/2 x √6 + 1/(√2/√3)
= 3/2 x √6 + 1/(√6/3)
= 3/2 x √6 + 3/√6
= 3/2 x √6 + (3/√6 ) x (√6/√6)
= 3/2 x √6 + 3√6/6
= 3/2 x √6 + √6/2
= √6 x ( 3/2 + 1/2)
= √6 x ( 2)
= 2√6
2a.) 1/√6
= ( 1/√6 ) x (√6/√6)
= √6/6
2b.) 4√6/3 - 2/√6
= 4√6/3 - 2 x (1/√6 )
= 4√6/3 - 2 x (√6/6 )
= 4√6/3 - 2√6/6
= 8√6/6 - 2√6/6
= 6√6/6
= √6
3.) 9/√12 - √32/6
= (9/√12 ) x (√12/√12) - {√[(4^2) x 2]}/6
= 9√12 /12 - 4√2/6
= 9{√[(2^2) x 3]}/12 - 2√2/3
= 18√3/12 - 2√2/3
= 3√3/2 - 2√2/3
= 9√3/6 - 4√2/6
= (9√3- 4√2)/6

Answer 4

1a.) 將 √2/√3有理化
ANS:√2/√3
=√2x√3 /√3 X √3
=√6/3
1b.) 化簡 3/2 x √6 + √3/√2
ANS:3/2 x √6 + √3/√2
=(3 x √6)/2+(√3 X√2) / (√2X√2)
=3√6 / 2 + √6/2
=4√6/2
2a.)將1/√6有理化
ANS:1/√6
=1X√6 /√6X√6
=√6/6
2b.) 化簡4√6/3 - 2/√6
ANS:4√6/3 - 2/√6
=4√6/3 -(2X√6)/√6X√6
=4√6/3 -2√6/6
=8√6/6 -2√6/6
=6√6/6
=√6
3.)9/√12 - √32/6
ANS:9/√12 - √32/6
=9X√12 /√12 x√12 - √32/6
=9√12 /12- √32/6
=9√12 /12- 2√32/12 (我只係做到依部咋,唔知點計下去)
P.S你最好寫番分數,會明D GA