Question

Find the smallest number by which 1458 must be multiplied so as to get a perfect square? also find square root of the number?

Answer 1

factorize 1458 n start do paring.
factor of 1458= 2×3×3×3×3×3×3.
so smallest no is 2 that should be multipled to get perfect square.
so perfect square will be 2916,
N square root will be 54.

Answer 2

Answer:

The required smallest number by 1458 must be multiplied so as to get a perfect square is 2.

The required square root of the number is 54.

Step-by-step explanation:

To find : The smallest number by which 1458 must be multiplied so as to get a perfect square also find square root of the number?

Solution :

First we factorize the number,

$1458= 2\times 3\times 3\times 3\times 3\times 3\times 3$

To get the perfect square we pair in two numbers,

$1458= 2\times 3^2\times 3^2\times 3^2$

Only 2 is left in pairing which means we require 2 to make it a perfect square.

Therefore, The required smallest number by 1458 must be multiplied so as to get a perfect square is 2.

Now, We find the square root

Multiply both side by 2,

$1458\times 2= 2\times 3^2\times 3^2\times 3^2\times 2$

$2916= 2^2\times 3^2\times 3^2\times 3^2$

$2916= (2\times 3\times 3\times 3)^2$

$2916= (54)^2$

Taking root both side,

$\sqrt{2916}= 54$

Therefore, The required square root of the number is 54.