Exercises: Square Roots

What we are looking for is the result of $\sqrt{56}$, i.e. a number that, if you multiply by itself, becomes $56$. Now, $56$ is not a square number. But there are square numbers that are close to $56$.

$49=7\cdot 7$

$$$64=8\cdot 8$

$56$ lies between the square numbers $49$ and $64$, which means that the value of $\sqrt{56}$ must lie between $7$ and $8$.

The square numbers $49$ and $64$ are approximately equidistant from $56$. For this reason, the value of the root is close to $7.5$.

$\sqrt{56}\approx 7.5$