In scientific notation numbers are written in the form #x xx10^n#, where #n# is an integer and #x# is in limits #[1,10)# i.e. #1<=x<10#.

Examples#:-#

#53246.6# is written as #5.32466xx10^4#

#46870000# is written as #4.687xx10^7#

#0.0007925# is written as #7.925xx10^-4#

#0.0000213# is writen as #2.13xx10^-5#

To extract square root of such numbers

(a) if n is even just take the square root of #x# and #10^n# and multiply them; and

(b) if #n# is odd, mutiply #x# by #10# and reduce #n# by #1# to make it even and then take square root of each and multiply them.

Hence

#sqrt(5.32466xx10^4)=sqrt5.32466xxsqrt(10^4)=2.3075xx10^2#

#sqrt(4.687xx10^7)=sqrt46.87xxsqrt(10^6)=6.846xx10^3#

#sqrt(7.925xx10^-4)=sqrt(7.925)xxsqrt(10^(-4))=2.815xx10^-2#

#sqrt(2.13xx10^-5)=sqrt21.3xxsqrt(10^(-6))=4.625xx10^-3#