The distance between two towns is 12875 km. Express this distance in standard form.

Question

ScanSolve AI Tutor · Accepted Answer

To make a number a perfect square, all the exponents in its prime factorization must be even.

Write down the prime factorization of 252.
The problem states that $252 = 2^2 \times 3^2 \times 7$ .
Examine the exponents of the prime factors.
The prime factor 2 has an exponent of 2 (even).
The prime factor 3 has an exponent of 2 (even).
The prime factor 7 has an exponent of 1 (odd).
Determine what factor is needed to make all exponents even.
To make the exponent of 7 even, we need to multiply by another 7. This will change $7^1$ to $7^1 \times 7^1 = 7^2$ .
So, the number to be multiplied is 7.
Verify the new product.
$252 \times 7 = (2^2 \times 3^2 \times 7) \times 7 = 2^2 \times 3^2 \times 7^2$ .
All exponents (2, 2, 2) are now even, so the product is a perfect square.

The least number that should be multiplied by 252 to make the product a perfect square is 7.

The correct option is D.
$\boxed{\text{D. 7}}$

Answer