Question

Simplify the following \[625\div 25\]

Answer 1

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.