Question

Find the smallest number by which 1800must be multiplied so that it become perfect square. Also find the square root of perfect square so obtained

Answer 1

1800 = 2 |1800
2 |900
2 |450
3 |225
3 |75
5 |25
5 |5
| 1
=2×2×2×3×3×5×5
=so we should multiply it by 2
=2×2×3×5
=60

Answer 2

Concept:

A number can be expressed as the product of its prime components through the process of prime factorization. A number with exactly two elements, 1 and the number itself, is said to be a prime number.

Given information:

Number $1800$ is given.

To find:

The smallest number by which 1800must be multiplied so that it become perfect square. Also find the square root of perfect square so obtained.

Solution:

The number $1800$ is given.

Find the prime factors of the given number.

$1800= 2*2*2*3*3*5*5$

The Pairs are formed of $2,3,5$ but single $2$ is left out of the prime factors.

Therefore, the smallest number to be multiplied by $1800$ is $2$.

The perfect square then obtained is $3600$.

Square root of $3600$ is $60$.

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