# Squares and Cube Roots Class 8 RS Aggarwal Exe-3F MCQs Goyal Brothers ICSE Maths Solutions

Squares and Cube Roots Class 8 RS Aggarwal Exe-3F MCQs Goyal Brothers Prakashan ICSE Foundation Maths Solutions Ch-3. We provide step by step Solutions of cisce prescribe publications to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-8 Mathematics.

## Squares and Cube Roots Class 8 RS Aggarwal Exe-3F MCQs Goyal Brothers ICSE Maths Solutions

 Board ICSE Publications Goyal Brothers Prakshan Subject Maths Class 8th writer RS Aggarwal Book Name Foundation Ch-3 Squares and Squire Roots, Cubes and Cube Roots Exe-3F MCQs on Squares and Cube Roots Edition 2024-2025

### Squares and Squire Roots, Cubes and Cube Roots

Squares and Cube Roots Class 8 RS Aggarwal Exe-3F MCQs Goyal Brothers Prakashan ICSE Foundation Maths Solutions Ch-3

Page- 54,55

#### Exercise- 3F

MCQs on Squares and Squire Roots, Cubes and Cube Roots

##### Que-1: How many perfect squares lie between 120 and 300 ?

(a) 5   (b) 6   (c) 7   (d)8

Solution- (c) 7

Reason : (11)2 = 121 (Greater than 120 but less than 300)
(17)2 = 289 (Greater than 120 but less than 300)
(18)2 = 324 (Greater than 120 but not less than 300)
∴ We have 7 (11 to 17) numbers between 120 and 300 which are perfect squares.

##### Que-2: √[41 – √{21 + √(19 – √9)}] = ?

(a) 3     (b) 5   (c) 6    (d) 6.4

Solution- (c) 6

Reason :√41−√21+√19−3
= √41−√21+√16
= √41−√21+4
= √41−√25
= √41−5
= √36 = 6.

##### Que-3: The value of √0.01 + √0.81 + √1.44 + √0.0009 is

(a) 2.03   (b) 2.1    (c) 2.11    (d) 2.23

Solution- (d) 2.23

Reason: √0.01+√0.81+√1.44+√0.0009
= √1/100+√81/100+√144/100+√9/10000
= √1/√100+√81/√100+√144/√100+√9/√10000
= 1/10 + 9/10 + 12/10 + 3/100
= 0.1 + 0.9 + 1.2 + 0.03 = 2.23

##### Que-4:  If 52/x = √(169/289), then the value of is

(a) 52    (b) 58   (c) 62   (d) 68

Solution- (d) 68

Reason : 52/x = √169/289
⇒ 52/x = √13²/17²
⇒ 52/x = 13/17
⇒ 13x = 52×17                   [cross multiplication]
⇒ x = (52×17)/13
⇒ x = 68

##### Que-5: ? ÷ √0.25 = 25

(a) 12.5   (b) 25   (c) 50    (d) 125

Solution- (a) 12.5

Reason : let’s solve √0.25 first
√0.25 = 0.5
let the no. be x
x/0.5 = 25
x = 25 x 0.5
x = 12.5

##### Que-6: For what value of * the statement (*/15) (*/135) = 1 is true ?

(a) 15   (b) 25    (c) 35    (d) 45

Solution- (d) 45

Reason : Let the missing number be x.
Then, x² = 15×135
⇔ x = √(15×135)
= √(15²×3²)
= 15×3 = 45.

##### Que-7: What percentage of the numbers from 1 to 50 have squares that end in the digit 1 ?

(a) 10  (b) 5    (c) 11    (d) 20

Solution- (d) 20

Reason : The numbers from 1 to 50 that have their squares ending in digit 1 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, i.e. 10 in numbers
∴ Required percentage = 10/50 × 100 = 20%

##### Que-8: Which of the following cannot be the unit digit of a perfect square number ?

(a) 1    (b) 6    (c) 8   (d) 9

Solution- (c) 8

Reason :Perfect square → Unit place digit
1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81
10² = 100
We can see number which can comes to unit place of perfect squares are 1,4,5,6,9 and 0.
∴ The numbers which can not come to the unit place of perfect square are 8.

##### Que-9:  √288/√128 = ?

(a) √3/2   (b) 3/√2   (c) 3/2   (d) 1.49

Solution- (c) 3/2

Reason :  √288/√128
= √(288/128)
= √9/4 = 3/2

##### Que-10: √72 x √98 = ?

(a) 42   (b) 64   (c) 74   (d) 84

Solution- (d) 84

Reason : √72 x √98 = √(2 x 2 x 2 x 3 x 3) x √(2 x 7 x 7)
= √(2 x 2 x 2 x 2 x 3 x 3 x 7 x 7)
= 2 × 2 × 3 × 7
= 84

##### Que-11: The least number by which 294 must be multiplied to make it a perfect square, is

(a) 2   (b) 3  (c) 6   (d) 24

Solution- (c) 6

Reason : 294 = 7 x 7 x 2 x 3.
To get a perfect square, it has to be multiplied by 2 x 3 i.e., 6.
∴ Required number = 6.

##### Que-12: The least number by which 1470 must be divided to get a number which is a perfect square, is

(a) 5   (b) 6  (c) 15   (d) 30

Solution- (d) 30

Reason : 1470 = 7 × 7 × 5 × 6.
To get a perfect square, it must be divided by 5 × 6, i.e., 30.

##### Que-13: What is the least number to be added to 7700 to make it a perfect square ?

(a) 44    (b) 77    (c) 98     (d) 131

Solution- (a) 44

Reason : √7700 ​≈ 87.7496
Rounding up to the next integer gives us 88. So, the next perfect square after 7700 is
88² = 7744.
Now, to find the least number to be added to 7700 to make it a perfect square, we subtract 7700 from 7744:
7744 − 7700 = 44.
So, the least number to be added to 7700 to make it a perfect square is 44.

##### Que-14:  √110.25 x √0.01 ÷ √0.0025 – √420.25 equals

(a) 0.50   (b) 0.64   (c) 0.73    (d) 0.75

Solution- (a) 0.50

Reason:  √110.25 ​: This is the square root of 110.25, which is 10.5.
√0.01 ​: This is the square root of 0.01, which is 0.1.
√0.0025 ​: This is the square root of 0.0025, which is 0.05.
√420.25 ​: This is the square root of 420.25, which is 20.5.
Now, let’s substitute these values into the expression:
√110.25 × √0.01 ÷ √0.0025 − √420.25.​
= 10.5 × 0.1 ÷ 0.05 − 20.5.
= 1.05 ÷ 0.05 − 20.5
= 21 − 20.5
= 0.5.

##### Que-15: The greatest four digit perfect square number is

(a) 9000  (b) 9801    (c) 9900   (d) 9981

Solution- (b) 9801

Reason: The largest four-digit number is 9999.
The square root of 9999 is approximately 99.995, which means the largest perfect square less than 9999 is 99² = 9801.
So, the greatest four-digit perfect square number is 9801.

##### Que-16: A gardener plants 17956 trees in such a way that there are as many rows as there are trees in a row. The number of trees in a row is

(a) 134    (b) 136    (c) 144  (d) 154

Solution- (a) 134

Reason: Let the number of rows = x
Number of columns = x
Total trees = 17956
x × x = 17956
x² = 17956
x = √17956
x = √(2×2×67×67)
x = 2×67
x = 134
Therefore, the number of trees on a rows =134.

##### Que-17: ∛4*(12/125) = ?

(a) 1*(2/5)  (b) 1*(3/5)  (c) 1*(4/5)  (d) 2*(2/5)

Solution- (b) 1*(3/5)

Reason: ∛4*(12/125) = ∛512/125 = ∛512/∛125
⇒ 512 = 2³ × 2³ × 2³
⇒ ∛512 = 2×2×2 = 8
⇒ 125 = 5³
⇒ ∛125 = 5
∴ ∛512/∛125 = 8/5 = 1*(3/5)

##### Que-18: By what least number must 21600 be multiplied so as to make it a perfect cube ?

(a) 6   (b) 10    (c) 20   (d) 30

Solution- (b) 10

Reason: 21600 can be factorized as 6×6×6×10×10
To make it perfect cube, it must be multiplied by 10

##### Que-19: What is the smallest number by which 3600 be divided to make it a perfect cube ?

(a) 9    (b) 50   (c) 300     (d) 450

Solution- (d) 450

Reason: 3600 can be written as 2^4 3^2 5^2
∴ To make it perfect cube divide it by 2 × 3²×5²
⇒ 450

— : End of Squares and Cube Roots Class 8 RS Aggarwal Exe-3F MCQs Goyal Brothers Prakashan ICSE Foundation Maths Solutions :–