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

True, according to the Power of a Power Property.
True, according to the Power of a Power Property.

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

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

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

Answer 1

To evaluate the equation \( 612 \cdot (6 - \sqrt{3}) = 36 \), let's first analyze each side.

1. The left side, \( 612 \cdot (6 - \sqrt{3}) \), consists of multiplying the number \( 612 \) by \( (6 - \sqrt{3}) \).
2. The right side is simply \( 36 \).

Let's approximate \( \sqrt{3} \) first. We know \( \sqrt{3} \) is approximately \( 1.732 \).

So, \( (6 - \sqrt{3}) \) is approximately:

\[ 6 - 1.732 \approx 4.268. \]

Now, multiplying \( 612 \) by \( 4.268 \): \[ 612 \cdot 4.268 \approx 2616.216. \]

Definitely, \( 2616.216 \neq 36 \).

Thus, the original equation \( 612 \cdot (6 - \sqrt{3}) = 36 \) is false.

Regarding the responses, the appropriate choice would be:

False, because the exponents should be multiplied. (This option is somewhat misleading in context but is technically correct regarding the structure of false statements in mathematical expressions. The issue is not really about exponents in this case, as the equation is fundamentally false due to incorrect multiplication rather than exponentiation, making it somewhat off-topic.)

The more correct statement would actually include verification of numerical value rather than exponents.