Question

Упростить выражение 4-√11-√99+√44 2√3-√12+√75 5√13-√52+√117

Answer 1

Resheniye na fotografii

Answer 2

1) 4-2√11
2) 5√3
3) 6√13

Answer 3

To simplify the given expression, we'll simplify each radical separately and then combine like terms.

1. Simplify √11, √99, and √44: √11 ≈ 3.31662479 √99 = √(9 * 11) = 3 * √11 ≈ 3 * 3.31662479 ≈ 9.94987437 √44 = √(4 * 11) = 2 * √11 ≈ 2 * 3.31662479 ≈ 6.63324958

2. Simplify 2√3, √12, and √75: 2√3 ≈ 2 * 1.73205081 ≈ 3.46410162 √12 = √(4 * 3) = 2 * √3 ≈ 2 * 1.73205081 ≈ 3.46410162 √75 = √(25 * 3) = 5 * √3 ≈ 5 * 1.73205081 ≈ 8.66025404

3. Simplify 5√13, √52, and √117: 5√13 ≈ 5 * 3.60555128 ≈ 18.02775638 √52 = √(4 * 13) = 2 * √13 ≈ 2 * 3.60555128 ≈ 7.21110255 √117 = √(9 * 13) = 3 * √13 ≈ 3 * 3.60555128 ≈ 10.81665383

Now, we can rewrite the expression with the simplified values:

(4 - 9.94987437 + 6.63324958) / (3.46410162 - 3.46410162 + 8.66025404) + (18.02775638 - 7.21110255 + 10.81665383)

Next, simplify within the parentheses:

(0.68337521) / (8.66025404) + (21.63330766)

Finally, perform the division and addition:

0.07886931 + 21.63330766 ≈ 21.71217697

Therefore, the simplified value of the expression is approximately 21.7122.