Question

The smallest number by which 1000 should be multiplied so as to get a perfect square
is

Answer 1

$\green{\bold{\underline{\underline{Question}}}}$

The smallest number by which 1000 should be multiplied so as to get a perfect square is ?

$\green{\bold{\underline{\underline{ToFind}}}}$

• Smallest number should be multiplied to make 1000 as perfect square

$\green{\bold{\underline{\underline{Solution}}}}$

Now,

=> 1000 = 2 × 2 × 2 × 5 × 5 × 5

=> 2² × 5² × 10

=> √(2² ×5² × 2 × 5)

=> 100√10

Hence,

=> 1000 should be multiplied by 10 to get a perfect square.

Answer 2

Answer:

The smallest number by which 1000 should be multiplied so as to get a perfect square =  10

Step-by-step explanation:

Given number is 1000

Required to find the smallest number to be multiplied to get a perfect square

Recall the concept

Perfect squares are numbers that can be expressed and the product of an integer by itself

Solution:

Given number is 1000

The prime factorization of 1000 = 2 × 2 × 2 × 5 × 5 × 5.

Combining we get,

1000 = 2²×5²×2×5

= 10²×10

1000 =  10²×10

$\sqrt{1000} = \sqrt{10^2 X10}$

$\sqrt{1000} = 10\sqrt{10}$

In the square root of 1000, we can see that 10 is an integer and $\sqrt{10}$ is an irrational numbers

Hence, if we multiply 10²×10 by 10

The factorization becomes 10²×10², and the number becomes a perfect square.

Hence,

The smallest number by which 1000 should be multiplied so as to get a perfect square =  10

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