Question

Find the value of $\sqrt{7}$ upto six decimal places by long division method

Answer 1

To find the value of $\sqrt{7}$ upto six decimal places by long division method:

Steps:

$1.$ Write $7$ as $7.000000000000$.

Consider the number in pairs from the right. So $7$ stands alone.

$2.$ Now divide $7$ with a number such that number $\times$ number gives $7$ or a number lesser than that. We determine $2\times 2=4$.

$3.$ Complete the division process. Obtain $2$ as the quotient and $3$ as the remainder. Bring down the first pair of zeros.

$4.$ Double the quotient obtained. Now $2\times 2=4$ forms the new divisor in the tens place.

$5.$ Find a number which, in the units place along with $40$, fetches the product $300$ or a number lesser than that.

$6.$ We find that $6\times 46$ gives $276$. Complete the division and get the remainder as $24$.

$7.$ Now our quotient is $2.6$. Double this with considering the decimal point and get $52$ as our new divisor.

$8.$ Bring down the next pair of zeros. Find the number that with $520$ gives $2400$ or a number lesser than that.

We conclude $4\times 524=2096$.

Repeat the same division process until we get the quotient approximated to $6$ digits.

Then we get $\sqrt{7}$ upto six decimal places $2.645751$ approximately.