Question

The area of a square field is $729$ square feet (sq. ft.). What is the side length of square field?

• A. $33$
• B. $37$
• C. $23$
• D. $27$

Answer 1

The correct option is D $27$

Given:
Area of square field $=729$ sq. ft.

To Find:
Side length of square field

As given in the hint, the area of the square field is ${\text{side}}^2.$

$\therefore$ Side length $=\sqrt{\text{Area}}=\sqrt{729}\text{ft.}$

Let's find the $\sqrt{729}$ using the long division method.

Step 1:
Place a bar over the pair of numbers starting from the unit place or right side of the number.
$\overline{7}\overline{29}.$

Step 2:
Take the largest number as the divisor whose square is less than or equal to the number on the extreme left of the dividend $\left(7\right).$ Divide and write the quotient. Here the quotient is $2$ and the remainder is $3.$


Step 3:
Next, we bring down the number, which is under the bar, to the right side of the remainder. Here, we bring down $29.$ So, $329$ is our new dividend.


Step 4:
Now, double the value of the quotient and enter it with a blank on its unit place.


Step 5:
Next, we have to select the largest digit for the unit place of the current divisor $(4-)$ such that the new divisor, when multiplied by the new digit at its unit place, is equal to or less than the current dividend $\left(329\right).$
In this case, $4\underset{–}{7}\times \underset{–}{7}=329.$ So the unit's place digit is $7.$

Step 6:
Finally, the remainder is $0,$ and we have no number left for division, therefore, the square root of $729$ is the final quotient, i.e., $\sqrt{729}=27.$

$\therefore$ The side length of square field with area $729$ square feet is $\underset{–}{27\text{feet}}$.

Hence, option (d.) is the correct one.