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

Answer 1

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)))#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Nathan Axel

To write ( a^{1.5} ) in radical form, you can express it as ( \sqrt{a^3} ).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.