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

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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**

(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 **