How do you change the expression #5^(1/2)# to radical form?

Answer 1

#5^(1/2)=color(blue)(sqrt(5))#

This is basically a definition: #color(white)("XXX")b^(1/a)=root(a)(b)#

To see why this is a reasonable definition consider that in general #color(white)("XXX")b^(2k)=b^k*b^k#

In the case of #5^(1/2)# #color(white)("XXX")5=5^1=(5^(1/2))*(5^(1/2))# that is #color(white)("XXX")5^(1/2)# must be a value which when multiplied by itself is equal to #5# and since #sqrt(5)*sqrt(5)=5#, the primary solution to this is #color(white)("XXX")5^(1/2)=sqrt(5)#

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Answer 2

Eva Abramson

To change the expression (5^{1/2}) to radical form, you rewrite it as the square root of 5. So, (5^{1/2}) is equivalent to (\sqrt{5}).

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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.