Name: Proving Pythagoras Theorem
Uploaded: 2019-07-19
Duration: 3 min 43 s
Description: In this video, we will learn the Pythagoras theorem and the method of proving the Pythagoras theorem by using geometry and algebraic identities in detail.

Question

Find the square root of $9025$ by division method.

Accepted Answer

Given number is $9025$ .

Step $1$ : Pair the digits of the given number, starting from units place to the left. Place a bar on each pair as shown below.

$90 25$

Step $2$ : Find the largest number whose square is less than or equal to $90$ such that $9^{2} < 90$ .

Step $3$ : Consider $9$ as the divisor and the quotient. Perform division and the remainder obtained is $9$ .

$\begin{matrix} 9 \\ 9 & 9 & 0 & 2 & 5 \\ - & 8 & 1 \\ 9 \end{matrix}$

Step $4$ : Bring down the second pair to the right of the Remainder.

Now, $925$ is the dividend.

$\begin{matrix} 9 \\ 9 & 9 & 0 & 2 & 5 \\ - & 8 & 1 \\ 9 & 2 & 5 \end{matrix}$

Step $5$ : Double the quotient i.e. $(9 \times 2 = 18)$ and write to the left of $925$ .

$\begin{matrix} 9 \\ 9 & 9 & 0 & 2 & 5 \\ - & 8 & 1 \\ 18 & 9 & 2 & 5 \end{matrix}$

Step $6$ : Guess the largest possible digit in the Ones place as $b$ such that $18 b \times b$ is equal to the new dividend $925$ . So, we have $b = 5$ . Perform division in which $925$ is the dividend, $185$ is the divisor and $5$ is the quotient.

$\begin{matrix} 9 & 5 \\ 9 & 9 & 0 & 2 & 5 \\ - & 8 & 1 \\ 185 & 9 & 2 & 5 \\ - & 9 & 2 & 5 \\ 0 \end{matrix}$

$\Rightarrow \sqrt{9025} = 95$

$∴$ The square root of $9025 = 95$

Find the square root of $9025$ by division method.

Important Questions on Square Roots and Cube Roots

Learn and Prepare for any exam you want !

Find the square root of 9025 by division method.

Important Questions on Square Roots and Cube Roots

Learn and Prepare for any exam you want !

Find the square root of $9025$ by division method.