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 smallest number by which $2400$ is to be multiplied to get a perfect square and also find the square root of the resulting number.

Accepted Answer

Given number is $2400$ . We need to find the smallest number by which the given number to be multiplied to get a perfect square.

Working of prime factorization:

$\begin{array}{l} 2 & 2400 \\ 2 & 1200 \\ 2 & 600 \\ 2 & 300 \\ 2 & 150 \\ 3 & 75 \\ 5 & 25 \\ 5 & 5 \\ 1 \end{array}$

$\Rightarrow 2400 = (2 \times 2) \times (2 \times 2) \times (5 \times 5) \times 2 \times 3$

So, we need to multiply the given number by $(2 \times 3)$ as this factor does not exist as pair in order to obtain a perfect square.

Therefore, the perfect square so obtained is $2400 \times (2 \times 3) = 2^{2} \times 2^{2} \times 2^{2} \times 3^{2} \times 5^{2} = {(2 \times 2 \times 2 \times 3 \times 5)}^{2}$

$\Rightarrow 2400 \times (2 \times 3) = 14400 = 120^{2}$ , which is the resulting number.

$\Rightarrow \sqrt{14400} = \sqrt{120^{2}} = 120$

Hence, $6$ is the smallest number to be multiplied by which the given number is a perfect square and the square root of the resulting number is $120$ .

Find the smallest number by which $2400$ is to be multiplied to get a perfect square and also find the square root of the resulting number.

Important Questions on Square Roots and Cube Roots

Learn and Prepare for any exam you want !

Find the smallest number by which 2400 is to be multiplied to get a perfect square and also find the square root of the resulting number.

Important Questions on Square Roots and Cube Roots

Learn and Prepare for any exam you want !

Find the smallest number by which $2400$ is to be multiplied to get a perfect square and also find the square root of the resulting number.