#### Answer

5.657 cm

#### Work Step by Step

$4^2+4^2=x^2$
$16+16=x^2$
$32=x^2$
$\sqrt {32}=x$
$\sqrt {32}$ is between $\sqrt {25}=5$ and $\sqrt {36}=6$
Divide by one of the square roots and average.
$32\div5=6.4$
$(5+6.4)\div2=5.7$
Repeat
$32\div5.7=5.614$
$(5.614+5.7)\div2=5.657$