Is the equation 612⋅(6–√)3=36

Question

true or false? Select the response that correctly answers the question and provides the appropriate justification.(1 point)
Responses

False, because the exponents should be divided.
False, because the exponents should be divided.

False, because the exponents should be multiplied.
False, because the exponents should be multiplied.

True, according to the Product Property.
True, according to the Product Property.

True, according to the Power of a Power Property.

Answer 1

To determine whether the equation \( 612 \cdot (6 - \sqrt{3}) = 36 \) is true or false, let's first simplify both sides.

Starting with the left-hand side:

1. Break down the expression \( 612 \cdot (6 - \sqrt{3}) \):
   • \( 612 = 6 \cdot 6 \cdot 17 = 36 \cdot 17 \)
   • Thus, it's \( 36 \cdot (6 - \sqrt{3}) \).

Now consider the expression \( (6 - \sqrt{3}) \):

• We can calculate \( 6 - \sqrt{3} \). The value of \( \sqrt{3} \) is approximately \( 1.732 \), so \( 6 - \sqrt{3} \approx 6 - 1.732 \approx 4.268 \).

2. Now, multiplying this by \( 36 \):
   • \( 36 \cdot (6 - \sqrt{3}) \approx 36 \cdot 4.268 \approx 153.648 \).

Now, let's look at the right-hand side of the equation:

• The right-hand side is simply \( 36 \).

Since \( 153.648 \) is not equal to \( 36 \), the given equation \( 612 \cdot (6 - \sqrt{3}) = 36 \) is false.

Therefore, the correct answer is:

False, because the exponents should be multiplied.