Answer:
Exact length = 2*sqrt(137) cm
Approximate length = 23.409 cm
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Work Shown:
Use the Pythagorean theorem
a^2 + b^2 = c^2
8^2 + 22^2 = c^2
64 + 484 = c^2
548 = c^2
c^2 = 548
c = sqrt(548)
c = sqrt(4*137)
c = sqrt(4)*sqrt(137) ..... use the rule sqrt(x*y) = sqrt(x)*sqrt(y)
c = 2*sqrt(137) .... this is the exact length
c = 23.4093998214392 ... use your calculator to find the approximate length
c = 23.409
I rounded to three decimal places, but feel free to round however you want. Or be sure to follow any rounding instructions your teacher provides.