Question

Which is equivalent to √(56c^16) / (162c^3) after it has been simplified completely?

A) (2^7c^8) / (3^4c^3)
B) 2c^4 / 3
C) (7√2c^4) / 3
D) (7c^4) / 3√2

Answer 1

To simplify √(56c16) / (162c3), we factor numbers and take out powers of c that can be rooted. After canceling and simplifying, we end up with option C: (7√2c4) / 3 being the equivalent and simplified expression.

Step-by-step explanation:

The student is asking to simplify the expression √(56c16) / (162c3). Let's begin by factoring the numbers and expressing the variables with exponents that can be taken out of the square root.

√(56c16) can be rewritten as √(23 × 7 × c16). Since we know that √(c16) = c8, we can take c8 out of the square root. Now we have √(23 × 7) × c8.

For the denominator, 162 can be factored as 2 × 34, so we have (2 × 34c3). Now we can rewrite the expression as (√(23 × 7) × c8) / (2 × 34c3) and simplify further.

The √(23 × 7) simplifies to √(8 × 7) which is √(22 × 2 × 7) and becomes (2 × √(2 × 7)). After canceling out common factors and simplifying the powers of c, we get:

(2 × √(2 × 7) × c8) / (2 × 34c3)

This simplifies to (2c4 × √(2 × 7)) / 34 which can be written as (7√2c4) / 3, which corresponds to option C: (7√2c4) / 3.