# Chapter 6 - Test - Page 464: 23

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 $32\div5.7=5.614$ $(5.614+5.7)\div2=5.657$

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