Square Root And Cube Root Test - 2

⇒x²   =  √331776

⇒x²  = 576

⇒x = √576

⇒x = 24

 (5.4756)^1/2 = 2.34
 

To find the cube root of 0.000729, we recognize that 0.000729 can be expressed as (0.09)³ .
Therefore, the cube root of 0.000729 is 0.09, which confirms that option 1  (0.09), is the correct 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 = 2 x 2 x 3 x 3 x 7 x 7 x 11 x 11 = 213444

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

= 12/14

= 0.85

►  Using identity, (a-b)²  = a²  + b²  - 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

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.
 

Squaring both side,
⇒0.0576 x a = 0.0576
⇒a = 1

Squaring both side,

⇒0.000256 x a = 2.56

⇒a = 2.56/0.000256

⇒a = 10000