Number of Significant Figures in Result of Square Root

Theorem

Let $m$ be a numbers which is presented to $d$ significant figures.

Then the most significant figures that $\sqrt m$ can have is also $d$.

Proof

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Examples

Significant Figures of $\sqrt {38 \cdotp 7}$

$\sqrt {38 \cdotp 7} = 6\cdotp 22$

Sources

• 1972: Murray R. Spiegel and R.W. Boxer: Theory and Problems of Statistics (SI ed.) ... (previous) ... (next): Chapter $1$: Computations