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# Simplify the following $625\div 25$

Last updated date: 22nd Jul 2024
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Hint: Here we have to find $625\div 25$. We can find out very easily by easy simplification. We know that we can write $625$ as the square of $25$i.e., $625={{25}^{2}}$. After doing some easy calculations we will get the final answer.

Complete step-by-step solution:
From the question it is clear that we have to find the value of $625\div 25$.
Let us assume the final value to be $x$.
finding the value of $x$ is similar as finding the value of$625\div 25$,
so,
$\Rightarrow x=625\div 25$……………..(1)
We can also write equation (1) as $x=\dfrac{625}{25}$
$\Rightarrow x=\dfrac{625}{25}$…………(2)
So now let us try to find the value of $x$.
From the standard values of square root value of $625$ is $25$ i.e., $\sqrt{625}=25$
$\Rightarrow \sqrt{625}=25$
Now do squaring on both sides, we get
$\Rightarrow {{\left( \sqrt{625} \right)}^{2}}={{25}^{2}}$…………….(3)
from the basic concepts of mathematics, we know${{\left( \sqrt{x} \right)}^{2}}=\pm x$.
So, we can write ${{\left( \sqrt{625} \right)}^{2}}$ as $\pm 625$
But in the question, we are asked to find only $+625$. So, we have to write only ${{\left( 625 \right)}^{2}}=+625$
So now we can write equation (3) as
$\Rightarrow +625={{25}^{2}}$
Now put $625={{25}^{2}}$ in equation (1)
So, equation (2) becomes as
$\Rightarrow x=\dfrac{625}{25}$
$\Rightarrow x=\dfrac{{{25}^{2}}}{25}$
Now write ${{25}^{2}}$ as $25\times 25$
$\Rightarrow x=\dfrac{25\times 25}{25}$
After simplification, we get
$\Rightarrow x=25$
So, we got the final $x$ value as $25$.
Now we can conclude that the value of $625\div 25$ is equal to $25$.

Note: Students should avoid mistakes while solving this problem. Students should also be aware of calculation mistakes while solving this problem. If a small mistake is made, then the final answer may get interrupted. So, students should avoid these mistakes while solving this problem such that the final answer can be obtained in a correct manner.