Question

why is sqrt7/7 = 1/sqrt7 ?

Been reading through all the rules of exponents and radicals...and still can't piece together why this is....

Answer 1

It's better to flip it backwards. 1/sqrt7 = sqrt7/7

Answer 2

most people (teachers) don't want sqrt in the bottom (denominator)

Answer 3

so you multiply 1/sqrt7 by sqrt7/sqrt7. The two sqrt7's turn into the 7. then the 1*sqrt7 turns into sqrt7 on the top.

Answer 4

sorry i would write it out, but I'm not at my normal computer.

Answer 5

oh wait I see now that you get this by rationalizing the denominator , this question i'm on though says to express 1/sqrt 7 as an exponent..is this possible?

Answer 6

a can be written as \(\sqrt a.\sqrt a\)
so 7 can be written as \(\sqrt 7.\sqrt 7\)
hence
\(\huge\frac{\sqrt 7}{7}=\frac{\sqrt 7}{\sqrt 7.\sqrt 7}=\frac{1}{\sqrt 7}\)

Answer 7

yes, sqrt7 is the same thing as saying (7)^(1/2)

Answer 8

ah I see now, so its basically what the book was talking about with the properties of nth roots or no?

Answer 9

mmm yes I guess you could say that. 3rd root of 7 would be (7)^1/3

Answer 10

sqrt's are basically fractional exponents.

Answer 11

ah okay I get it now hah, Thank you!!

Answer 12

np gl