What values of a and b make the equation true?√(648) = √(2^a × 3^b)
a = 3, b = 2
a = 2, b = 3
a = 3, b = 4
a = 4, b = 3

Solution:

As we know that √648 is not a perfect square.

Therefore, we will use the prime factorization method to find the values of a and b.

Since 648 is a composite number, it has prime factors.

Thus,

648 can be expressed as the product of its prime factors.

648 = 2 × 2 × 2 × 3 × 3 × 3 × 3

The Exponential Notation of 648 = 2³ × 3⁴

Hence,

√648 = √(2³ × 3⁴)

Therefore, 3rd option is Correct.

What values of a and b make the equation true?
√(648) =√(2^ᵃ × 3^ᵇ)

Summary:

The values of a and b for the equation √(648) = √(2^a × 3^b) is a = 3 and b = 4.