# Aptitude - Squares & Cubes Examples

Q 1 - √ 2025 = ?

A - 45

B - 35

C - 34

D - 30

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
```

Q 2 - √ 54 x √ 6 = ?

A - 24

B - 15

C - 18

D - 13

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

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

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

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

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

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

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

```9261 = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 3 x 3