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QUESTION: 1

Solution:

⇒ x^{2 }= √331776

⇒ x^{2} = 576

⇒ x = √576

⇒ x = 24

QUESTION: 2

Solution:

(5.4756)^{1/2} = 2.34

QUESTION: 3

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

Solution:

QUESTION: 4

The cube root of 0.000729 is

Solution:

QUESTION: 5

What is the least perfect square which is divisible by each of 21, 36 and 66?

Solution:

**► **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 = 2 x 2 x 3 x 3 x 7 x 7 x 11 x 11 = 213444

QUESTION: 6

Solution:

*= *(12/11) x (11/15) x (15/14)

= 12/14

= 0.85

QUESTION: 7

Solution:

**► **Using identity, (a-b)^{2} = a^{2} + b^{2} - 2ab

**► **Here a = √7 and b = 1/√7

= (√7)^{2 }+ (1/√7)^{2} - 2. √7.1/√7

= 7 + 1/7 - 2

= 5 + 1/7

= 36/7

QUESTION: 8

The square root of 16641 is:

Solution:

**Step 1**:

- We now need to obtain the digital root of the number. Here's how you do it:
- Split the number up and add each digit together:

1 + 6 + 6 + 4 + 1 = 18 - If the answer is more than one digit, you would add each digit of the answer together again:

1 + 8 = 9 - What is the digital root of number 16,641?

Answer: 9

**Step 2:**

- So now we know the digital root of 16,641 is 9. Is 9 in the list of digital roots that are always a square root (1, 4, 7 or 9)?
- Answer: YES, 9 is in the list of digital roots that are always perfect squares. We can conclude that 16,641 could be a perfect square!

**Factoring**

- OK, so now we know that 16,641 could be a perfect square. We have to find the factors of the number to be sure.
- Here are all of the factors of 16,641:

(1 x 16,641) (3 x 5,547) (9 x 1,849) (43 x 387) (129 x 129)

Hence the answer is **129.**

QUESTION: 9

Solution:

Squaring both side,

⇒ 0.0576 x a = 0.0576

⇒ a = 1

QUESTION: 10

Solution:

Squaring both side,

⇒ 0.000256 x a = 2.56

⇒ a = 2.56/0.000256

⇒ a = 10000

### Problem Set 1 : Square Root and Cube Root - Quantitative Aptitude

Video | 07:42 min

### Problem Set 2 : Square Root and Cube Root - Quantitative Aptitude

Video | 08:46 min

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