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2022 IIMC keystage3-IWYMIC individual Question 15

xIMC · 2022 IIMC keystage3-IWYMIC individual

Question 15

Let $\overline{abcd}$ be a four-digit number, where $a,c\ne0$, such that $\frac{\sqrt{\overline{abcd}}}{\sqrt{\overline{ab}}+\sqrt{\overline{cd}}}$ is a rational number. Find all possible value(s) of $\overline{abcd}$.