Name: Patterns of Square Numbers
Uploaded: 2019-07-19
Duration: 9 min 26 s
Description: Did you know that square numbers form various patterns? The square of any odd natural number apart from 1 can be expressed as the sum of two consecutive natu...

Question

Find the least number which must be added to $520$ to make it a perfect square.

Accepted Answer

Given number is $520$ , which is not a perfect square. We need to find the least number to be added to $520$ so that the resultant number is a perfect square.

Perform division method to find the square root of the perfect square nearest to $520$ as follows:

$\begin{matrix} 2 & 2 \\ 2 & 5 & 2 & 0 \\ - & 4 \\ 42 & 1 & 2 & 0 \\ - & 8 & 4 \\ 3 & 6 \end{matrix}$

$\Rightarrow 22 < \sqrt{520}$

$\Rightarrow 22^{2} < 520 < 23^{2}$

So, we need to consider $23^{2} = 23 \times 23 = 529$

Now, the difference between $529$ and $520$ is $(529 - 520) = 9$ .

$\Rightarrow (520 + 9) = 23^{2}$ , which is the required perfect square.

Hence, $9$ is the least number which must be added to $520$ to make it a perfect square.

Find the least number which must be added to $520$ to make it a perfect square.

Important Questions on Squares and Square Roots

Learn and Prepare for any exam you want !

Find the least number which must be added to 520 to make it a perfect square.

Important Questions on Squares and Square Roots

Learn and Prepare for any exam you want !

Find the least number which must be added to $520$ to make it a perfect square.