Question

What is the square root of 100000?

Answer 1

Hint: We can write 100000 as $${10}^5$$. A square of a number ‘$$a$$’ is a number such that $$a=x^2$$, in other words, a number $$x$$ whose square root of $$a$$.now we have to find the square root of 100000. Square root of $$100000$$ can be written as $$\sqrt{100000}$$

Complete step-by-step answer:
From the given question it is clear that we have to find the square root of $$100000$$.
When we are trying to find the square root of a number, the number should be a positive number because we cannot write a negative number under the square root. If we write a negative number under the square root, we will get a complex number. But we want real numbers.
As we are given a positive number, we can write $$100000$$ under the square root.
Let us consider$$a=100000$$
Now we have to find the square root of $$a=100000$$. let it be $$x$$
So, we can write
 $$\Rightarrow x=\sqrt{100000}$$
we can write 100000 as $${10}^5$$.
$$\Rightarrow x=\sqrt{{10}^5}$$
From the basic concept of mathematics, we can write
$$x^n=x^{n_1+n_2+n_3........+n_n}$$ where $$n=n_1+n_2+n_3.............+n_n$$
So, we can write $$\sqrt{{10}^5}=\sqrt{{10}^{2+2+1}}$$
$$\Rightarrow x=\sqrt{{10}^{2+2+1}}$$
We can also write $$x^{a+b+c}=x^a\times x^b\times x^c$$
$$\Rightarrow x=\sqrt{{10}^2\times {10}^2\times {10}^1}$$…………….(1)
From the basic concept of mathematics, we can also write
$$\sqrt{n_1\times n_2\times n_3.........\times n_n}=\sqrt{n_1}\times \sqrt{n_2}\times \sqrt{n_3}.........\times \sqrt{n_n}$$
So now we can write $$\sqrt{{10}^2\times {10}^2\times {10}^1}=\sqrt{{10}^2}\times \sqrt{{10}^2}\times \sqrt{{10}^1}$$

So, the equation becomes
$$\Rightarrow x=\sqrt{{10}^2}\times \sqrt{{10}^2}\times \sqrt{{10}^1}$$
On simplification we get
$$\Rightarrow x=10\times 10\times \sqrt{10}$$
Om multiplication of $$10$$and $$10$$ we get $$100$$
$$\Rightarrow x=100\times \sqrt{10}$$
We know the standard value of $$\sqrt{10}=3.16227766$$
$$\Rightarrow x=10\times 10\times 3.16227766$$
On further simplification, we get
$$\Rightarrow x=316.227766$$
$$x=316.227766$$ is the root of $$100000$$.

Note: Students should avoid calculation mistakes. Because while doing calculations even a small calculation error can lead to major error while finding the root of $$100000$$. Students should know the applications of the square root.