Question

$\sqrt{784}$ by long division method.

Answer 1

To find the square root of $784$ using long division method, we need to follow the steps:

Step 1:

Write $784$ as shown in the figure. Start pairing the digits from the right end in pairs of two by putting a bar on top of them. So, we got two pairs of $7$ and $84$

Step 2:

Now find a number $n$ such that $n\times n$ is a number less than equal to $7$.

Hence, $n=2,(2\times 2=4)$.

Step 3:

Now subtract the obtained value from the first pair in the dividend and add the divisor with itself $(n+n)$

i.e., $(2+2=4)$.

Now bring the second pair down $84$.

Step 4:

The new dividend is $384$. Double the quotient to get the first digit of the new divisor. The digit in the tens place will be $4$..

Step 5:

Find the digit at the units place of divisor such that when it gives number less than equal to $384$.

Step 6:

The number is 8. Now we get our new divisor as $48$.

$48\times 8=384$.

Complete the division and get the remainder. We finally get $0$. Thus, the process of division completes here.

Hence, $\sqrt{784}=28$.