能力傾向測試 - 平方與立方示例

答案 - A

解釋

Resolve 2025 into prime numbers first.
2025 = 5 x 5 x 3 x 3 x 3 x 3 = 52 x 32 x 32
∴ √2025 = 5 x 3 x 3 = 45

答案 - C

解釋

√ 54 x √ 6 = √ 54 x 6 = √ (3 x 3 x 6 x 6)
= √ (32 x 62)
= √ 18

答案 - D

解釋

√(248 + √(51 + √169)) = √(248 + √(51 + 13))
= √(248 + √(64)) = √(248 + 8) = √(256) = 16

答案 - B

解釋

√(25/16) = √25/ √ 16 = 5/4.

答案 - B

解釋

√(5/3) = (√5 / √ 3) x (√3 / √ 3) =  √15 / 3 = 3.88/ 3 = 1.293

答案 - B

解釋

√13.69 + √0.1369 + √ 0.001369 + √ 0.00001369 
= √(1369 / 100) + √(1369/ 10000) + √(1369/ 1000000) + √(1369/ 100000000)
= √1369 / √100 + √1369 / √10000 + √1369 / √1000000 + √1369 / √100000000
= 37/10 + 37/100 + 37/1000 + 37/ 10000 
= 3.7 + 0.37 + 0.037 + 0.0037 
 = 4.1107 

答案 - A

解釋

(√5 + √3)/(√5 - √3) 
= (√5 + √3)/(√5 - √3) * (√5 + √3)/(√5 + √3)
= (√5 + √3)2/(5 - 3)
= (5 + 3 + 2√5 + √3)/2 
= (8 + 2√15)/2
= 2(4 + √15)/2
= 4 + √15
= 4 + 3.8729
= 7.8729

答案 - A

解釋

9261 = 3 x 3 x 3 x 7 x 7 x 7
= 33 x 73
∴ ∛9261 = (33 x 73)1/3
= 3 x 7 = 21.

答案 - C

解釋

9261 = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 3 x 3
= 23 x 33 x 32 x 5
∴ required no: 3 x 52 = 3 x 25 = 75