Question

Simplify the following $$625÷25$$

Answer 1

Hint: Here we have to find $$625÷25$$. 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 $$625÷25$$.
Let us assume the final value to be $$x$$.
finding the value of $$x$$ is similar as finding the value of$$625÷25$$,
so,
$$\Rightarrow x=625÷25$$……………..(1)
We can also write equation (1) as $$x={\displaystyle \frac{625}{25}}$$
$$\Rightarrow x={\displaystyle \frac{625}{25}}$$…………(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
$$\Rightarrow x={\displaystyle \frac{625}{25}}$$
$$\Rightarrow x={\displaystyle \frac{{25}^2}{25}}$$
Now write $${25}^2$$ as $$25\times 25$$
$$\Rightarrow x={\displaystyle \frac{25\times 25}{25}}$$
After simplification, we get
$$\Rightarrow x=25$$
So, we got the final $$x$$ value as $$25$$.
Now we can conclude that the value of $$625÷25$$ 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.