Question

Approximate 137√
13
7
, correct to four decimal places, by using a sequence of values that gets closer and closer to 7–√
7
. (1 point)
Responses

885.5582
885.5582

872.5904
872.5904

2.6457513
2.6457513

885.6688

Answer 1

To approximate \( 137\sqrt{13}\) using the value of \(\sqrt{7}\), we can perform some calculations.

First, we'll calculate \( \sqrt{7} \):

\[
\sqrt{7} \approx 2.6457513
\]

Next, we can calculate \( 137\sqrt{13} \). We first need \( \sqrt{13} \):

\[
\sqrt{13} \approx 3.605551
\]

Using this calculated \( \sqrt{13} \):

\[
137 \sqrt{13} \approx 137 \times 3.605551 \approx 493.605
\]

This indicates we approximated incorrectly as we should be looking to use \( \sqrt{7} \) to find answers closer to a different comparison.

To approximate \( \sqrt{7} \) to four decimal places, we already have:

\[
\sqrt{7} \approx 2.6458
\]

Given the context of the options you provided, 885.5582, 872.5904, 2.6457513, and 885.6688 do not correlate directly with \( 137\sqrt{13} \) or its approximations.

Let's find \( 137 \) multiplied by either approximation:

If we directly compute \( 137 \) times \( \sqrt{7} \):

\[
137 \times 2.6458 \approx 362.4816
\]

If we are looking precisely at \( 137 \cdot \sqrt{13} \approx 493.605\).

Given that the numerical value compared to \( \sqrt{7} \) requires careful approximation, it seems none of your specific provided outputs (885.5582, 872.5904, 885.6688) are numerically near any related approximation by \( 7 \).

Thus, if we must end at using \(\sqrt{13}\):

The answer among options related would be:

**2.6457513**, which is the actual computed root of 7.

For \( 137\sqrt{13} \):

- The sought value \( \sqrt{7} \) yield finding values near \( 493.605\).

So unless corrected, for four decimal places \( \sqrt{7} \approx 2.6458 \).