Question

Formula to find number of natural numbers between 2 perfect squares .​

Answer 1

Answer:

Try this - let x and be two numbers then find z= [sqrt(xy)], next find p= [sqrt(z)]. Now p^2 is the required square.

Example: need to find perfect square between 8717 and 9587.

Step 1: z = sqrt(8717*9587) = 9141.

Step 2: p= [sqrt(9141)] = [95.61] = 95.

So 95^2 = 9025 is reqd square

Answer 2

Answer:

The formula to find the number of natural numbers between 2 perfect squares is 2n.

To Find,

The formula

Solution,

The number of natural numbers lying between two consecutive perfect square numbers is 2n. 

where n = n² and (n+1)²

Now, let's take an example to understand this concept better.

Example: How many natural numbers lie between 1111² and 1112²?

(A) 2257

(B) 2222

(C) 2356

(D) 2500

⇒ we know that the number of natural numbers lying between two consecutive perfect square numbers is 2n. 

So, 1111²

and

(1111 + 1)²

So, the number of natural numbers = 2n

Where n = 1111

= 2 × 1111

= 2222.

The correct answer is option b.

The formula to find the number of natural numbers between 2 perfect squares is 2n.

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