1. **State the problem:** We are given a list of numbers and asked to square each number and then add all the squared values together. 2. **Formula used:** To square a number $x$, we calculate $x^2$. To find the sum of squares for numbers $x_1, x_2, ..., x_n$, we compute $$\sum_{i=1}^n x_i^2$$ 3. **Calculate each square:** $22.8^2=519.84$ $25.8^2=665.64$ $23.5^2=552.25$ $20.7^2=428.49$ $20.8^2=432.64$ $24.7^2=610.09$ $27^2=729$ $22.5^2=506.25$ $21^2=441$ $28.5^2=812.25$ $22.6^2=510.76$ $24.5^2=600.25$ $20.9^2=436.81$ $18.9^2=357.21$ $16.1^2=259.21$ $19.5^2=380.25$ $17.8^2=316.84$ $22.6^2=510.76$ $24.4^2=595.36$ $17.6^2=309.76$ $21.9^2=479.61$ $22.6^2=510.76$ $25.1^2=630.01$ $18.7^2=349.69$ $24.2^2=585.64$ $23.1^2=533.61$ $18.4^2=338.56$ $21.1^2=445.21$ $18.6^2=345.96$ $18.3^2=334.89$ $19.3^2=372.49$ $22.8^2=519.84$ $18.1^2=327.61$ $15.4^2=237.16$ $23.6^2=556.96$ $21.2^2=449.44$ $17.8^2=316.84$ $16.8^2=282.24$ $20.3^2=412.09$ $18.6^2=345.96$ 4. **Sum all squared values:** $$519.84 + 665.64 + 552.25 + 428.49 + 432.64 + 610.09 + 729 + 506.25 + 441 + 812.25 + 510.76 + 600.25 + 436.81 + 357.21 + 259.21 + 380.25 + 316.84 + 510.76 + 595.36 + 309.76 + 479.61 + 510.76 + 630.01 + 349.69 + 585.64 + 533.61 + 338.56 + 445.21 + 345.96 + 334.89 + 372.49 + 519.84 + 327.61 + 237.16 + 556.96 + 449.44 + 316.84 + 282.24 + 412.09 + 345.96 = 16388.92$$ 5. **Final answer:** The sum of the squares of the given numbers is **16388.92**.