Name: Estimation of Square Roots
Uploaded: 2019-07-19
Duration: 6 min 2 s
Description: For not-perfect squares, we can estimate their square root to the closest whole number. Learn how to estimate the square root of non-perfect squares.

Question

Find the square root of

729

.

Accepted Answer

Given number is $729$ .

We have to find the square root of given number.

By using long division method, to find the square root.

Step $1$ : Put a bar over each pair of digits starting from the digit at one's place. Thus, we have, $7 29$ .

Step $2$ : Find the largest number whose square is less than or equal to the number under the extreme left bar $(2^{2} < 7 < 3^{2})$ , here it is $2$ . Divide and get the remainder ( $1$ in this case).

Step $3$ : Bring down the number under the next bar to the right of the remainder. So new dividend is $329$ .

Step $4$ : Double the quotient and enter it with a blank on its right.

Step $5$ : Guess the largest possible digit to fill the blank which will also become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the product is less than or equal to the dividend.

In this case $47 \times 7 = 329$ , so we choose the new digit as $7$ . Get the remainder.

Step $6$ : Since the remainder is $0$ and no digits are left in the given number, therefore $\sqrt{729} = 27$

Thus,

$\begin{matrix} 2 & 7 \\ 2 & 7 & 2 & 9 \\ - & 4 \\ 47 & 3 & 2 & 9 \\ - & 3 & 2 & 9 \\ 0 \end{matrix}$

Hence, the square root of $729$ is $27$ .

Find the square root of $729$ .

Important Questions on Squares and Square Roots

Learn and Prepare for any exam you want !

Find the square root of 729.

Important Questions on Squares and Square Roots

Learn and Prepare for any exam you want !

Find the square root of $729$ .