When sqrt(0.005) is written as a decimal, what is the hundredth digit?

Question

The answer is of course 7 but the thing is I am not allowed to use calculators to solve this. Can you show me the fast method?

Answer 1

Because the decimal number system is a positional number system, each digit is multiplied by the position value (for example, hundredth) of the position in which it is found.

 

What happens when you square fractions ?

 

    number                    square

     0,100                      0.0100

     0.090                      0.0081

     0.080                      0.0064

        ...                            ...

     0.070                      0.0049

     0.060                      0.0036

     0.050                      0,0025

     0.040                      0.0016

     9.010                      0.0001

 

We know that the number which is the square root of 0.005 is somewhere between 0.070 and 0.080.  The digit in the hundredths place is a 7.

 

Note how one place in the number results in twp places in the square; or two places in a number compares to one place in the square root.  Since 0.0050 is between the squares of 0.07 and 0.08, the hundredths place is 7.

Answer 2

Let x be the square root.  Rewrite the equation as

 

x² = 0.005

 

x² - 0.005 = 0

 

Now use the quadratic formula.