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**sploder12** · 03-31-2021, 01:20 PM

We can linearize the sqrt(x) at x = 4 to get the line y - 2 = 1/4(x - 4)
by plugging in 5 to this line we get y - 2 = 1/4(5-4) which simplifies to y = 1/4 + 2
therefore sqrt(5) is about 2.25, however this is an overestimate since sqrt(x) is concave down for the entire interval for which it is defined.

Or just plug it into a calculator and get 2.2360679775...

03-31-2021, 01:20 PM	#3
sploder12 JS Enjoyer Join Date: Jul 2016 Posts: 68	Re: what's the square root of 5 We can linearize the sqrt(x) at x = 4 to get the line y - 2 = 1/4(x - 4) by plugging in 5 to this line we get y - 2 = 1/4(5-4) which simplifies to y = 1/4 + 2 therefore sqrt(5) is about 2.25, however this is an overestimate since sqrt(x) is concave down for the entire interval for which it is defined. Or just plug it into a calculator and get 2.2360679775...