Quantitative_Problems on Root and Cube Root

Quantitative Section Problems on Square Root and Cube Root

www.crackcmat.com

www.crackcmat.com Page 2

Contents Formulaes: ............................................................................................................................................. 3

Problems ................................................................................................................................................. 4


Formulaes:

1. Square Root:

If x2 = y, we say that the square root of y is x and we write y = x.

Thus, 4 = 2, 9 = 3, 196 = 14.

2. Cube Root:

The cube root of a given number x is the number whose cube is x.

We, denote the cube root of x by x.

Thus, 8 = 2 x 2 x 2 = 2, 343 = 7 x 7 x 7 = 7 etc.

Note:

1. xy = x x y

2. xy

= x

= x

x y

= xy

.y y y y


Problems 1. The cube root of .000216 is:

A. .6 B. .06

C. 77 D. 87

Answer & Explanation

Answer: Option B

Explanation:

(.000216)1/3 = 216 1/3106

=

6 x 6 x 6 1/3102 x 102 x 102

=

6 102

= 6

100

= 0.06

View Answer Workspace Report Discuss in Forum

2.

What should come in place of both x in the equation x

= 162

.128 x

A. 12 B. 14

C. 144 D. 196


Answer: Option A

Explanation:

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.


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

A. 213444 B. 214344

C. 214434 D. 231444


Answer: Option A

Explanation:

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


4. 1.5625 = ?

A. 1.05 B. 1.25

C. 1.45 D. 1.55


Answer: Option B

Explanation:

1|1.5625( 1.25 |1 |------- 22| 56 | 44 |------- 245| 1225 | 1225


|------- | X |-------

1.5625 = 1.25.


5. If 35 + 125 = 17.88, then what will be the value of 80 + 65 ?

A. 13.41 B. 20.46

C. 21.66 D. 22.35


Answer: Option D

Explanation:

35 + 125 = 17.88

35 + 25 x 5 = 17.88

35 + 55 = 17.88

85 = 17.88

5 = 2.235

80 + 65 = 16 x 5 + 65

= 45 + 65

= 105 = (10 x 2.235) = 22.35 6. If a = 0.1039, then the value of 4a2 - 4a + 1 + 3a is:

A. 0.1039 B. 0.2078

C. 1.1039 D. 2.1039


Answer: Option C

Explanation:

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


7. If x =

3 + 1and y =

3 - 1 , then the value of (x2 + y2) is:

3 - 1 3 + 1

A. 10 B. 13

C. 14 D. 15


Answer: Option C

Explanation:

x = (3 + 1)

x (3 + 1)

= (3 + 1)2

= 3 + 1 + 23

= 2 + 3. (3 - 1) (3 + 1) (3 - 1) 2

y = (3 - 1)

x (3 - 1)

= (3 - 1)2

= 3 + 1 - 23

= 2 - 3. (3 + 1) (3 - 1) (3 - 1) 2

x2 + y2 = (2 + 3)2 + (2 - 3)2

= 2(4 + 3)

= 14


8. 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:

A. 57 B. 67

C. 77 D. 87


Answer: Option C

Explanation:

Money collected = (59.29 x 100) paise = 5929 paise.

Number of members = 5929 = 77.


9. The square root of (7 + 35) (7 - 35) is

A. 5 B. 2

C. 4 D. 35


Answer: Option B

Explanation:

(7 + 35)(7 - 35) = (7)2 - (35)2 = 49 - 45 = 4 = 2.


10. If 5 = 2.236, then the value of

5-

10+ 125 is equal to:

2 5

A. 5.59 B. 7.826

C. 8.944 D. 10.062


Answer: Option B


Explanation:

5-

10+ 125 =

(5)2 - 20 + 25 x 55

2 5 25

= 5 - 20 + 50

25

= 35

x 5

25 5

= 355

10

= 7 x 2.236

2

= 7 x 1.118

= 7.826


11.

625x

14x

11 is equal to:11 25 196

A. 5 B. 6

C. 8 D. 11


Answer: Option A

Explanation:

Given Expression = 25

x 14

x 11

= 5. 11 5 14


12. 0.0169 x ? = 1.3


A. 10 B. 100

C. 1000 D. None of these


Answer: Option B

Explanation:

Let 0.0169 x x = 1.3.

Then, 0.0169x = (1.3)2 = 1.69

x = 1.69

= 100 0.0169


13.

3 - 1 2

simplifies to:3

A. 34

B. 43

C. 43

D. None of these


Answer: Option C

Explanation:

3 - 1 2

= (3)2 +

1 2- 2 x 3 x

13 3 3

= 3 + 1

- 2 3

= 1 + 13

= 43


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

two-digit number is 8 ?

A. 1 B. 2


C. 3 D. None of these


Answer: Option D

Explanation:

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


15. The square root of 64009 is:

A. 253 B. 347

C. 363 D. 803


Answer: Option A

Explanation:

2|64009( 253 |4 |---------- 45|240 |225 |---------- 503| 1509 | 1509 |---------- | X |----------

64009 = 253.

Quantitative_Problems on Root and Cube Root

Documents

Transcript of Quantitative_Problems on Root and Cube Root