How do you write #a^1.5# in radical form?

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Answer 1 · 2017-01-08T15:51:28

See full explanation below:

Because #1.5 = 3/2# we can rewrite this expression as:

#a^(3/2)#

We can now use this rule for exponents to modify the expression:

#(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))# and #x^(color(red)(a) xx color(blue)(b)) = (x^color(red)(a))^color(blue)(b)#

#a^(color(red)(3)/color(blue)(2)) -> a^(color(red)(3) xx 1/color(blue)(2)) -> (a^(color(red)(3)))^(1/color(blue)(2))#

Now we can use this rule to put this in a radical form:

#x^(1/color(red)(n)) = root(color(red)(n))(x)#

#(a^(color(red)(3)))^(1/color(blue)(2)) -> root(color(blue)(2))(a^(color(red)(3))) -> sqrt(a^(color(red)(3)))#