calculating powers and square roots

Question

The variance and the standard deviation are related by the fact that the square root of the variance is equal to the standard deviation. Suppose the variance of the time it takes to complete a bachelor's degree is 0.8. Find the standard deviation. Round your answer to four decimal places.

Answer 1

standard deviation = sqr(variance) = sqr(.8) = 0.8944

use a calculator

had variance been .81 the square root would have been .9

as 9x9 = 81

.80 is slightly less than .81 so the square root of .80 should be slightly less than .9

a "guesstimate" might have been 0.89

there's also a long division type way to manually calculate a square root

first look for the largest digit which squared is less than .80. that's 8.

8x8 =64. 80-64= 16, bring down 2 more 0's to get 1600. double the 8 to get 16 add another digit such that 169 times 9 is less than 1600. 169x9 = 1521. subtract.

1600-1521 = 79 bring down two more zeros. 7900

double the 89 to get 178 add another digit at the end 1784 such that 4 x 1784 is less than 7900, continue the process for as many decimals as you need.

A sort of "surprise" is that the standard deviation is less than the variance. that's always true when the variance is less than one.