Estimate and compare square roots

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Learn it Find the two perfect squares on either side. To compare numbers like $3\sqrt{5}$ and $2\sqrt{11}$, square them (or move the outside number inside the root).

Example: Which is larger: $3\sqrt{5}$ or $2\sqrt{11}$?

$3\sqrt{5} = \sqrt{9 \times 5} = \sqrt{45}$.
$2\sqrt{11} = \sqrt{4 \times 11} = \sqrt{44}$.
$45 > 44$, so $3\sqrt{5}$ is larger.

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