Answer

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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.

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