適性-正方形と立方体の例

Q1 -√2025=?

A -45

B -35

C -34

D -30

Answer - A

Explanation

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

Q2 -√54x√6=?

A -24

B -15

C -18

D -13

Answer - C

Explanation

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

Q3 -√(248 +√(51 +√169))=?

A -15

B -12

C -13

D -16

Answer - D

Explanation

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

Q4 -√(25/16)=?

A -3 / 4

B -5 / 4

C -4

D -4 / 5

Answer - B

Explanation

√(25/16) = √25/ √ 16 = 5/4.

Q5 -√15= 3.88の場合。√(5/3)とは何ですか?

A -1.213

B -1.293

C -1.321

D -1.432

Answer - B

Explanation

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

Q6 -√1369= 37の場合、√13.69+√0.1369+√0.001369+√0.00001369とは何ですか?

A -4.0021

B -4.1107

C -3.1232

D -2.1323

Answer - B

Explanation

√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

Q7 -√15= 3.8729の場合、(√5+√3)/(√5-√3)とは何ですか?

A -7.8729

B -6.8729

C -5.8729

D -4.8729

Answer - A

Explanation

(√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

Q 8 - ∛9261=?

A -21

B -17

C -29

D -23

Answer - A

Explanation

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.

Q 9-パーファクトキューブを作成するために9720に乗算するために必要な最小数はいくつですか?

A -55

B -65

C -75

D -85

Answer - C

Explanation

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