If we are looking for the Pythagoras triple that goes with 5 and 7
Check
If the pythagoras is 7, then the third number would be
![\begin{gathered} a^2+5^2=7^2 \\ a^2+25=49 \\ a^2=49-25 \\ a^2=24 \\ a=\sqrt[]{24} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/crydylqylxewgsfg8s1p83yht6uriieq7f.png)
If the third number is the hypothenuse, then third number would be
![\begin{gathered} a^2=5^2+7^2 \\ a^2=25+49 \\ a^2=74 \\ a=\sqrt[]{74} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/suhg0e1hk0y0vjcy7g2pg8cy1dccrpoviq.png)
Please note that square root of 24 and the square root of 74 would not give a whole number.
Hence their is no whole number that goes with 5 and 7 to make a pythagoras triple