Question

What is the square root of 130?

Answer 1

Hint: The given question asks us to find the square root of 130. We do not actually have to calculate the square root of 130. We can find an approximate range between which 130 is present. We know that the squares of 11 and 12 are 121 and 144, that means the root of 130 lies between 11 and 12. We can further narrow it down by finding the square of 11.5, which is 132.25. So, we can see that the root of 130 lies between 11 and 11.5. we can further narrow it down until we get the square close to 130. Hence, we will have the square root of 130.

Complete step by step answer:
According to the given question, we are asked to find the square root of the given number. We can find the square root of the number without actually calculating the square root, that is, by using approximations.
We know that the squares of 11 and 12 are 121 and 144 respectively. So, we can see that the square root of 130 lies between 11 and 12.
But we require an almost exact number whose square is 130. So, we try to narrow down the range.
We know that the square of 11.5 is 132.25.
So, the square root of 130 lies between 11 and 11.5. we can see that 130 is more near to the square of 11.5.
Narrowing the range further, we know that the square of 11.3 is 127.69.
So, we can say that the square root of 130 is between 11.3 and 11.5.
That is, the square root of 130 is 11.4 approximately.
Square of 11.4 is 129.96.

Therefore, the square root of 130 is 11.4 approximately.

Note: We can use these types of approximations to narrow down the possible range of the square root of the given number. While using these approximations, a general idea of the squares of the common numbers must be known, else this method will prove very hard to do.