Form 3 有理數/無理數 Questions (20p)

1.
(√3 - √2)(7√2 + 5√3) - (5 - 2√6)(2√6 + 5)
= √3(7√2 + 5√3) - √2(7√2+ 5√3) - 5(2√6 + 5) + 2√6(2√6 + 5)
= 7√6 + 15 - 14 - 5√6 - 10√6 - 25 + 24 + 10√6
= 2√6


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2.
(5/√12) - (√18/7)
= (5/2√3) - (3√2/7)
= (35/14√3) - (6√6/14√3)
= (35 - 6√6)/14√3
= [(35 - 6√6)/14√3] ´ (√3/√3)
= (35√3 - 18√2)/42


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3.
(√3 + √2)[(1/√3) + (1/√2)]
= (√3 + √2)[(√2/√6) + (√3/√6)
= (√3 + √2)²/√6
= (5 + 2√6)/√6
= [(5 + 2√6)/√6] ´ (√6/√6)
= (12 + 5√6)/6

1.
(√3-√2)(7√2+5√3)-(5-2√6)(2√6+5)
=7√6+5*3-7*2-5√6-(25-4*6)
=2√6+15-14-(25-24)
=2√6+1-1
=2√6

2.
(5/√12)-(√18/7)
=(5/√12)(√12/√12)-(3√2/7)
=(10√3/12)-(3√2/7)
=(70√3-36√2)/84
=2(35√3-18√2)/84
=(35√3-18√2)/42

3.
(√3+√2)[(1/√3)+(1/√2)]
=(√3/√3)+(√3/√2)+(√2/√3)+(√2/√2)
=2+(√6/2)+(√6/3)
=2+(3√6+2√6)/6
=2+(5√6)/6