Question

. The smallest number by which 1000 should be multiplied so as to get a perfect square is (a) 5 (b) 10 (c) 4 (d) 8.

Answer 1

Answer:

if you multiply that all from 1000 than the answer is a=5000

b=10000

c=4000d=8000

Answer 2

(b) 10 is the correct answer.

Given:

• number is 1000.

To find:

• the smallest number to be multiplied to get a perfect square

Solution:

• Recall the concept Perfect squares are numbers that can be expressed and the product of an integer by itself.
• 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
• √1000 = 10√10
• In the square root of 1000, we can see that 10 is an integer and √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.

#SPJ2