Question

How do you write `sqrt37` in exponential form?

Answer 1

`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)`