Find your Math Personality!

Find your Math Personality!

# 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 = 2^{3} × 3^{4}

Hence,

√648 = √(2^{3} × 3^{4})

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.

Math worksheets and

visual curriculum

visual curriculum