ความถนัด - ตัวอย่างสี่เหลี่ยมและลูกบาศก์
คำถาม 1 - √ 2025 =?
ก - 45
B - 35
ค - 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
คำถาม 2 - √ 54 x √ 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
Q 3 - √(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
Q 4 - √(25/16) = ?
A - 3/4
B - 5/4
C - 4
D - 4/5
Answer - B
Explanation
√(25/16) = √25/ √ 16 = 5/4.
Q 5 - If √15 = 3.88. What is √(5/3)?
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
Q 6 - If √ 1369 = 37 then what is √13.69 + √0.1369 + √ 0.001369 + √ 0.00001369?
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
Q 7 - If √ 15 = 3.8729 then what is (√5 + √3)/(√5 - √3)?
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 - What is the least number required to multiply to 9720 to make a perfact cube?
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