Question

Simplify $\sqrt{83}$.

Answer 1

As $83$ is not a perfect square, we won’t get the square root of 83 as a whole number.

Now, $9^2<83<{10}^2$

That is, the square root of 83 must lie between $9$and$10$.

By long division method of finding the square root:

Step 1: Write$83$as $83.0000$ and make pairs of two from right to left.

Step 2: Now take $83$, since$9\times 9=81$ divide$83$ by $9$to get the remainder $2$.

Step 3: Now take down another pair i.e.$00$. We now have$200,$ divided it by 181 to get the remainder$19.$

Step 4: Again take down another pair and the above process
Hence,$\sqrt{83}$ $=9.11$ (approx).