7. (10 points) If a four-digit number $5 a b 4$ is a square of a number, then $a+b=$

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【Analysis】 $70^{2}=4900,80^{2}=6400,5000$ is a four-digit number more, so it should be the square of a two-digit number between 70 and 80. Also, its last digit is 4, so the unit digit of this two-digit number can only be 2 or 8. $72^{2}=5184$, which meets the requirement. We need to check if $78^{2}$ meets the requirement as well.

【Solution】Solution: $72^{2}=72 \times 72=5184$ meets the requirement. $78^{2}=78 \times 78=6084$, does not meet the requirement. Discard it.

So $a=1, b=8$.
$$
a+b=1+8=9 .
$$

Therefore, the answer is: 9 .