Estimate the sum of 5–√+7–√ by performing increasingly small rational approximations. Approximate the sum to four decimal places. (1 point) Responses 4.8819 4.8819 2.6458 2.6458 4.8818 4.8818 2.2361
To estimate the sum of 5–√+7–√ using rational approximations, we can start by approximating √5 and √7.
√5 is approximately 2.2361 (to four decimal places).
√7 is approximately 2.6458 (to four decimal places).
Now, we can substitute these approximations back into the original sum:
5–√ + 7–√ ≈ 5–2.2361 + 7–2.6458
≈ 2.7639 + 4.3542
≈ 7.1181
Therefore, the approximate sum of 5–√+7–√ is 7.1181.