If the square of a number is between 25 & 48, then the number is between ? and ?             

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durbanville's profile pic

durbanville | High School Teacher | (Level 2) Educator Emeritus

Posted on

To put your question in maths terms:

Let x= the number

`25<x^2<48`  as it cannot =25 or it cannot =48 if it is between them.

As `sqrt(25) = 5`  and  `sqrt(48)= 6.93`  (rounded to 2 decimals)

5.01 `<=`  x  `<=`  6.92 (rounding off to 2 decimals)

Please remember to only post one question at a time. Your questions were all unrelated so please post them separately.

`therefore` The number is between 5.01 and 6.92 or equal to them

vaaruni's profile pic

vaaruni | High School Teacher | (Level 1) Salutatorian

Posted on

(1) -> Given: square of a number is between 25 - 48

Solution :

Case 1: If the number is a positive integer then it will be between

Intger(square root of(25)) and Integer(square root of (49))

 since 48 is not a perfect square and the next perfect square is 49.

Hence the number will be between  5 and 7  <-- Answer

Case 2:If the number is an (+)  or (-) integer then it will be between

           -5  and 7 <--Answer

      [ since square root of 25 is (+5)  and (-5)

Case 3:If the number is positive  real number then it will be between

             5.0  and 6.928

Case 4:If the number is a (+) or (-) real number then it will be

          between -6.928  and +6.928 <-- Answer

Q2) There are 7 numbers which are perfect square including 1 and 54 

         [ they are : 1, 4, 9, 16, 25, 36, 49 ] therefore there are 7 ways

  by which any one of the number picked will be a perfect square  and

there are 54 ways by which any number 1 - 54 (both inclusive) can be

picked. Therefore probability of a number picked random will be a

perfect square = 7/54 = 0.129 <-- Answer

Q3) Every positive number >1 is greater than its  square root

  example : square root of 4 = (+2) and (-2) [4>2, 4>-2]

   Similarly  square root of 9 = (+3) and (-3)  [ 9>3, 9>-3]

  And the square root 1 is equal to 1

 Hence we can say that Every number is greater than or equal to

  its  square root  

From the example given we can also say the counter that is :

Square root of Every positive number is less than or equal to the

number 

 

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