In other words, the minute hand "overtakes" the hour hand on 44 occasions in 24 hours in order to give a 90 degree angle. Therefore the answer to your question is 44.
Step-by-step explanation: it would hit the first 90 degree angle when the hour is at twelve and the minutes at 15 then 12 and 45 then 3 and 30 and three and 12 then 6 and 15 and six and 30 then 9 and 30 then 9 and 12 .
You can subtract normally when the square roots are the same( like in your problem) but the squares stay they same and the numbers on the outside change.