Question

What is the square root of 8 to the ${{3}^{rd}}$ power?

Answer 1

Hint: For calculating this you should know about the digits till any power. That means that if any digit is given and it is given that you have to calculate it till any power. That means the digit will multiply by itself till how much time which is given the power. And then calculate for square root is take its under root and solve this until the last digit which is indivisible like 1.

Complete step by step answer:
It is asked in the question that we have to calculate the square root of 8 till its ${{3}^{rd}}$ power. It means that we have to calculate ${{8}^{3}}$ and then what the answer will come will take the square root of that digit. For calculating any digit, a till its power b (b is basically a positive or zero or negative integer) but generally it is a zero or positive number. So, we can write it as ${{a}^{b}}$. If we say that you have to calculate a to its ${{4}^{th}}$ power, then a is multiplied by itself till four times as,
$a\times a\times a\times a={{a}^{4}}$
Now if we take the square root of this then,
$\begin{align}
  & \Rightarrow \sqrt{{{a}^{4}}}=\sqrt{a\times a\times a\times a} \\
 & \Rightarrow \sqrt{{{a}^{4}}}=a\times a={{a}^{2}} \\
\end{align}$
So, the square root of a till its ${{4}^{th}}$ power is ${{a}^{2}}$. So, like that we have to calculate the square root of 8 till the ${{3}^{rd}}$ power of 8. So, we can write,
8 to the ${{3}^{rd}}$ power = ${{8}^{3}}$
$\begin{align}
  & =8\times 8\times 8 \\
 & =512 \\
\end{align}$
So, 8 to the ${{3}^{rd}}$ power is 512. Now we have to take the square root of 512 for calculating the square root of ${{8}^{3}}$. By taking the square root, we have,
$\begin{align}
  & \sqrt{512}=\sqrt{4\times 4\times 4\times 4\times 2} \\
 & \Rightarrow \sqrt{512}=16\sqrt{2} \\
 & \Rightarrow \sqrt{512}=16\times 1.414 \\
 & \Rightarrow \sqrt{512}=22.6274 \\
\end{align}$

So, the square root of 8 to the ${{3}^{rd}}$ power is equal to 22.6274.

Note: For calculating the square root of any digit till any power is not so much tough but you have to be very careful because there can be mistakes in the calculations for the power of any number mistake and if you are calculating for root, then also you have to be careful and determine the value till the last indivisible value and then solve it completely.