1. Find the following surd and express your answer as integar or fraction
(a) √4 76/81
(b) √98/162
2. Express the following surds in their simplest forms
(a) √7/11
(b) √8/27
3.Suppose √5 = a, √7 =b. express √320-√7/9 in term of a and b.
All steps please thx.
maths question
2006-10-16 1:13 am
回答 (4)
2006-10-16 1:25 am
✔ 最佳答案
1. (a) √(4 + 76 / 81)= √[(4 * 81 + 76) / 81]
= √[400 / 81]
= √400 / √81
= 20 / 9
(b) √(98 / 162)
= √(49 / 81)
= √49 / √81
= 7 / 9
2. (a) √(7 / 11)
= √7 / √11
= [√7 * √11] / [√11 * √11]
= (√77) / 11
(b) √(8 / 27)
= √8 / √27
= [√(4 * 2)] / [√(9 * 3)]
= [2√2] / [3√3]
= [2√2 * √3] / [3√3 * √3]
= (2√6) / 9
3. √320 - √(7 / 9)
= √(64 * 5) - (√7 / √9)
= √64 * √5 - (√7 / 3)
= 8√5 - (√7 / 3)
= 8a - (b / 3)
2006-10-17 2:44 am
1 (a).
√4 76/81
=√400/81
=√20²/9²
=√(20/9)²
=20/9
(b).
√98/162
=√49/81
=√7²/9²
=√(7/9)²
=7/9
2 (a).
√(7/11)
=√7/√11
=[(√7)(√11)]/[(√11)(√11)]
=(√(7×11)/(√11)²
=(√77)/11
(b).
√(8/27)
=√(24/81)
=(√24)/(√81)
=[√(4×6)]/9
=√4×√6/9
=(2√6)/9
3.
√320-√(7/9)
=√64×√5-√7/√9
=8√5-√7/3
=8a-b/3
√4 76/81
=√400/81
=√20²/9²
=√(20/9)²
=20/9
(b).
√98/162
=√49/81
=√7²/9²
=√(7/9)²
=7/9
2 (a).
√(7/11)
=√7/√11
=[(√7)(√11)]/[(√11)(√11)]
=(√(7×11)/(√11)²
=(√77)/11
(b).
√(8/27)
=√(24/81)
=(√24)/(√81)
=[√(4×6)]/9
=√4×√6/9
=(2√6)/9
3.
√320-√(7/9)
=√64×√5-√7/√9
=8√5-√7/3
=8a-b/3
參考: Calculation+Exploring Mathematics 3A Exercise 4C (5, 6, 11, 12, 14)
2006-10-16 2:33 am
1. (a) √(4 + 76 / 81)
= √[(4 * 81 + 76) / 81]
= √[400 / 81]
= √400 / √81
= 20 / 9
(b) √(98 / 162)
= √(49 / 81)
= √49 / √81
= 7 / 9
2. (a) √(7 / 11)
= √7 / √11
= [√7 * √11] / [√11 * √11]
= (√77) / 11
(b) √(8 / 27)
= √8 / √27
= [√(4 * 2)] / [√(9 * 3)]
= [2√2] / [3√3]
= [2√2 * √3] / [3√3 * √3]
= (2√6) / 9
3. √320 - √(7 / 9)
= √(64 * 5) - (√7 / √9)
= √64 * √5 - (√7 / 3)
= 8√5 - (√7 / 3)
= 8a - (b / 3)
= √[(4 * 81 + 76) / 81]
= √[400 / 81]
= √400 / √81
= 20 / 9
(b) √(98 / 162)
= √(49 / 81)
= √49 / √81
= 7 / 9
2. (a) √(7 / 11)
= √7 / √11
= [√7 * √11] / [√11 * √11]
= (√77) / 11
(b) √(8 / 27)
= √8 / √27
= [√(4 * 2)] / [√(9 * 3)]
= [2√2] / [3√3]
= [2√2 * √3] / [3√3 * √3]
= (2√6) / 9
3. √320 - √(7 / 9)
= √(64 * 5) - (√7 / √9)
= √64 * √5 - (√7 / 3)
= 8√5 - (√7 / 3)
= 8a - (b / 3)
參考: me
2006-10-16 1:25 am
(1a) √(4 76/81)
=(2√119)/9
(1b) √(98/162)
=(√98)/9√2
=(√49)/9
=7/9
(2a) √(7/11)
應該係最simplest的了..
除非佢要呢個
√(7/11)=( √7x√11)/11= (√77))/11
(2b) √(8/27)
=(2√2)/(3√3)
=(2√6)/(9)
3.Suppose √5 = a, √7 =b. express √320-√7/9 in term of a and b.
呢條唔係好明你係
-√7/9 定係-√(7/9 )
因為差好遠..
=(2√119)/9
(1b) √(98/162)
=(√98)/9√2
=(√49)/9
=7/9
(2a) √(7/11)
應該係最simplest的了..
除非佢要呢個
√(7/11)=( √7x√11)/11= (√77))/11
(2b) √(8/27)
=(2√2)/(3√3)
=(2√6)/(9)
3.Suppose √5 = a, √7 =b. express √320-√7/9 in term of a and b.
呢條唔係好明你係
-√7/9 定係-√(7/9 )
因為差好遠..
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