Final answer:
To make 8¹⁷²⁹×6¹⁹⁴⁷ a perfect square, it needs to be multiplied by 12.
Step-by-step explanation:
To find the least number that should be multiplied with 8¹⁷²⁹×6¹⁹⁴⁷ to make it a perfect square, we need to determine the factors of the given numbers and their exponents. Let's break it down.
8¹⁷²⁹ can be expressed as (2³)¹⁷²⁹. And 6¹⁹⁴⁷ can be expressed as (2×3)¹⁹⁴⁷.
To make it a perfect square, we need to ensure that both the exponents of 2 and 3 are even. Since the exponent of 2 is 1, it needs to be multiplied by 2 to become 2²=4. And the exponent of 3 is already 1, so it remains the same.
Therefore, the least number that should be multiplied with 8¹⁷²⁹×6¹⁹⁴⁷ to make it a perfect square is (2² × 3) = 12.