How many perfect squares lie between 120 and 300?

A perfect square is a number obtained when a whole number is multiplied by itself. For example, $11 \times 11 = 121$, so $121$ is a perfect square.

To find the starting point, determine which whole number squared gives a value just above $120$:

$10 \times 10 = 100$ (less than $120$)

$11 \times 11 = 121$ (greater than $120$)

The first perfect square is $11^2 = 121$.

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To find the ending point, determine which whole number squared gives a value just below $300$:

$17 \times 17 = 289$ (less than $300$)

$18 \times 18 = 324$ (greater than $300$)

The last perfect square is $17^2 = 289$.

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The perfect squares between $120$ and $300$ are:

$11^2 = 121$

$12^2 = 144$

$13^2 = 169$

$14^2 = 196$

$15^2 = 225$

$16^2 = 256$

$17^2 = 289$

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Counting these values gives $7$ perfect squares between $120$ and $300$.