Question 1

The cube root of .000216 is:

Accepted Answer

(.000216)1/3 = ❨ 216 ❩ 1/3 106 = ❨ 6 x 6 x 6 ❩ 1/3 102 x 102 x 102 = 6 102 = 6 100 = 0.06

Question 2

A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 59.29, the number of the member is the group is:

Accepted Answer

Money collected = (59.29 x 100) paise = 5929 paise. ∴ Number of members = √5929 = 77.

Question 3

If x = √3 + 1 and y = √3 - 1 , then the value of (x2 + y2) is: √3 - 1 √3 + 1

Accepted Answer

x = (√3 + 1) x (√3 + 1) = (√3 + 1)2 = 3 + 1 + 2√3 = 2 + √3. (√3 - 1) (√3 + 1) (3 - 1) 2 y = (√3 - 1) x (√3 - 1) = (√3 - 1)2 = 3 + 1 - 2√3 = 2 - √3. (√3 + 1) (√3 - 1) (3 - 1) 2 ∴ x2 + y2 = (2 + √3)2 + (2 - √3)2 = 2(4 + 3) = 14

Question 4

How many two-digit numbers satisfy this property.: The last digit (unit's digit) of the square of the two-digit number is 8?

Accepted Answer

A number ending in 8 can never be a perfect square.

Question 5

If √5 = 2.236, then the value of √5 - 10 + √125 is equal to: 2 √5

Accepted Answer

√5 - 10 + √125 = (√5)2 - 20 + 2√5 x 5√5 2 √5 2√5 = 5 - 20 + 50 2√5 = 35 x √5 2√5 √5 = 35√5 10 = 7 x 2.236 2 = 7 x 1.118 = 7.826

Question 6

❨ √625 x 14 x 11 ❩ is equal to: 11 √25 √196

Accepted Answer

Given Expression = 25 x 14 x 11 = 5. 11 5 14

Question 7

√0.0169 x? = 1.3

Accepted Answer

Let √0.0169 x x = 1.3. Then, 0.0169x = (1.3)2 = 1.69 ⟹ x = 1.69 = 100 0.0169

Question 8

The square root of 64009 is:

Accepted Answer

2|64009( 253
    |4
    |----------
  45|240
    |225
    |----------
 503|  1509
    |  1509
    |----------
    |     X
    |---------- 
 ∴ √64009 = 253.

Question 9

The square root of (7 + 3√5) (7 - 3√5) is

Accepted Answer

(7 + 3√5)(7 - 3√5) = (7)2 - (3√5)2 = √49 - 45 = √4 = 2.

Question 10

❨ √3 - 1 ❩ 2 simplifies to: √3

Accepted Answer

❨ √3 - 1 ❩ 2 = (√3)2 + ❨ 1 ❩ 2 - 2 x √3 x 1 √3 √3 √3 = 3 + 1 - 2 3 = 1 + 1 3 = 4 3

Question 11

The least perfect square, which is divisible by each of 21, 36 and 66 is:

Accepted Answer

L.C.M. of 21, 36, 66 = 2772. Now, 2772 = 2 x 2 x 3 x 3 x 7 x 11 To make it a perfect square, it must be multiplied by 7 x 11. So, required number = 22 x 32 x 72 x 112 = 213444

Question 12

What should come in place of both x in the equation x = √162 . √128 x

Accepted Answer

Let x = √162 √128 x Then x2 = √128 x 162 = √64 x 2 x 18 x 9 = √82 x 62 x 32 = 8 x 6 x 3 = 144. ∴ x = √144 = 12.

Question 13

If 3√5 + √125 = 17.88, then what will be the value of √80 + 6√5?

Accepted Answer

3√5 + √125 = 17.88 ⟹ 3√5 + √25 x 5 = 17.88 ⟹ 3√5 + 5√5 = 17.88 ⟹ 8√5 = 17.88 ⟹ √5 = 2.235 ∴ √80 + 6√5 = √16 x 5 + 6√5 = 4√5 + 6√5 = 10√5 = (10 x 2.235) = 22.35

Question 14

If a = 0.1039, then the value of √4a2 - 4a + 1 + 3a is:

Accepted Answer

√4a2 - 4a + 1 + 3a = √(1)2 + (2a)2 - 2 x 1 x 2a + 3a = √(1 - 2a)2 + 3a = (1 - 2a) + 3a = (1 + a) = (1 + 0.1039) = 1.1039

Question 15

√1.5625 =?

Accepted Answer

1|1.5625( 1.25
    |1
    |-------
  22| 56
    | 44
    |-------
 245| 1225
    | 1225
    |-------
    |    X
    |-------     
 ∴ √1.5625 = 1.25.

Question 16

Find the cube root of 19683.

Accepted Answer

In 19683, 19 lies between 23 and 33, so left digit is 2 and 683 ends with 3, so right digit is 7. thus 27 is a cube root of 19683.

Question 17

If √ y/169 = 54/39, then y is equal to?

Accepted Answer

√y/169= 54/39 ⇒ y/169 = (54/39) x (54/39) ∴ y= (54/39) x (54/39) x 169 = 324

Question 18

112/√196 x √579/12 x √256/8 =?

Accepted Answer

Given Expression 112/√196 x √579/12 x √256/8 =(112/14) x (24/12) x (16/8) = 32

Question 19

Given that √ 4096 = 64, the value of √ 4096 + √ 40.96 + √ .004096 is?

Accepted Answer

√4096 + √40.96 + √.004096 = √4096 + √4096/100 + √4096/1000000 =√4096 + √4096/10 + √4096/1000 = 64 + 64/10 + 64/1000 = 70.464

Question 20

√ .04

Accepted Answer

√.04 = √4/100 = 2/10 = 0.2

Square Root and Cube Root Questions