How do you write #sqrt37# in exponential form?

1 Answer
May 5, 2017

#37^(1/2)#

Explanation:

#" using "color(blue)"law of exponents"#

#• a^mxxa^n=a^((m+n))#

#a^(1/2)xxa^(1/2)=a^((1/2+1/2))=a^1=a#

#"also "a^(1/2)xxa^(1/2)=(a^(1/2))^2#

#rArr(a^(1/2))^2=a#

#color(blue)"take the square root of both sides"#

#sqrt((a^(1/2))^2)=sqrta#

#rArra^(1/2)=sqrtalarrcolor(red)" in general"#

#"Thus " sqrt37=37^(1/2)#