Given:
![\sqrt[]{2654}](https://img.qammunity.org/2023/formulas/mathematics/high-school/v6czm0mg67oxjdtscioqdhaxeet567b5wi.png)
The square root of a number is the inverse operation of the square operation of a number.
The square root of a number is the number that when multiplied by itself gives the original number as the result.
To find the square root of 2654, we have:
![\begin{gathered} \sqrt[]{2654} \\ \\ =51.5 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/dy2whc2qqf3bizn3blxiq80187qy85744n.png)
The number given, 2654 is not a perfect square.
A square root of a perfect square is a non decimal number.
Apply the formula:
![\begin{gathered} \sqrt[]{x}=\sqrt[]{y}+\frac{x-y}{2\ast\sqrt[]{y}} \\ \\ \text{Where y is the closest p}\operatorname{erf}ect\text{ square} \end{gathered}]()
y is the closest perfect square.
![\begin{gathered} \sqrt[]{2654}=\sqrt[]{2601}+\frac{2654-2601}{2\ast\sqrt[]{2601}} \\ \\ \sqrt[]{2654}=51+(2654-2601)/(2\ast51) \\ \\ \sqrt[]{2654}=51+(53)/(102) \\ \\ \sqrt[]{2654}=51+0.51=51.51 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/u3suo8i6o55ipxn98cvf3p1s4dmf5naldk.png)
If the number is a perfect square, the square root of the number would be a non decimal number.
ANSWER:
51.5