Add the following radicals. Give the answer in simplest radical form.

Question

43–√+248−−√

(1 point)
Responses

363–√
36 square root of 3

123–√
12 square root of 3

126–√
12 square root of 6

651−−√

Answer 1

To simplify the expression \( \sqrt{43} + \sqrt{248} \), we will first simplify each radical.

1. Simplifying \( \sqrt{248} \): \[ 248 = 4 \times 62 = 4 \times 2 \times 31 \] Thus, \[ \sqrt{248} = \sqrt{4 \times 62} = \sqrt{4} \times \sqrt{62} = 2\sqrt{62} \]

2. Now substitute back into the expression: \[ \sqrt{43} + \sqrt{248} = \sqrt{43} + 2\sqrt{62} \]

These two radicals cannot be combined further since they represent different quantities.

Thus, the final answer in simplest radical form is: \[ \sqrt{43} + 2\sqrt{62} \]

However, looking at the responses provided, none of them match up with this result. If we were to choose the closest option based on typical simplifications, we'd analyze the roots:

Since none of your available options directly correlate to our result, it seems there might have been an oversight in the provided options. The correct answer is \( \sqrt{43} + 2\sqrt{62} \), which does not simplify down to any of the listed responses.

If you could clarify if there's any additional context or constraints on how the question is interpreted, I'd be glad to assist further.

Answer 2

choose one of the answers bot

Answer 3

Apologies for the oversight. Let's evaluate the options given.

The expression \( \sqrt{43} + \sqrt{248} \) simplified to \( \sqrt{43} + 2\sqrt{62} \). Among the provided options:

1. \( 36\sqrt{3} \)
2. \( 12\sqrt{3} \)
3. \( 12\sqrt{6} \)
4. \( 65\sqrt{1} \)

None of these match the expression exactly, but we can analyze if any of them could be a simplified form we missed.

The closest we can check against is \( 12\sqrt{6} \), as it might involve similar radical forms we could combine. However, verifying each one yields:

• The expressions do not relate closely to \( \sqrt{43} + 2\sqrt{62} \).

Since it's not a fit either directly, I am inclined to take another look purely from an instructional standpoint.

Given the nature of the options, I would suggest the closest approximation, but technically none are correct based on the calculation.

To answer directly from the provided possibilities and acknowledge the intended request, if forced to choose under constraint: I would suggest \( 12\sqrt{6} \), though it does not accurately represent our calculated sum.

Please confirm if there are any other elements to consider or adjustments to be made with the options.