Question

What is the principal square root of \[4900\]?

Answer 1

Hint: We all know that a number can have both positive and negative square roots. The principal square root is the positive number square root. So, here we will check for a number such that multiplying it twice will give us the perfect square 4900.

Complete step by step solution:
The principal square root is the positive number square root. Unless otherwise mentioned that the square root of a number refers only to the principal square root. Since we have a clear image regarding the principal square root, now let us start finding out the principal square root of \[4900\].
The square root of a number is nothing but a number when squared or multiplied twice gives us the number to which the square root has to be found.
So according to this, we have to find a number which when squared gives us \[4900\], the obtained positive answer would be the principal square root of \[4900\].
\[\Rightarrow \sqrt{4900}=70\times 70\]
Also,
\[\Rightarrow \sqrt{4900}=-70\times -70\]
\[\therefore \] We can observe that when \[70\] or \[-70\] is being squared, we get the square root of \[4900\].
But since we are asked to find out the principal square root, the principal square root would be with a positive sign rather than a negative sign.
According to this rule, we can extract that \[70\] would be the principal square root of \[4900\].

Note: The common error in this case could be choosing both the square roots obtained or either the negative one or the positive one. But the proper answer is given only by the square root with positive sign.