[11(9) State whether each statement is true or false. cannot be positive 8 becau

Question

[11(9) State whether each statement is true or false. cannot be positive 8 because the exponent and the radical cancel each other. It should be True False b) If we are given any real number, that number has exactly one odd root and two even roots. True False c) We need to restrict the domains of nth root functions when n is an even integer, but these restrictions are not necessary when n is an odd integer. True False d) Using a calculator, we find that $-3125, so we can say that 5 is the fifth root of 3125 or 53125 True False e) If n is an odd integer and b is a negative number,thep Vbis not a real number f) The domain of f(x) Vx-4 is [4, 00). g) Vx2 is always x. True False True False True False True False i) The unlike radicals 3 2 and 5/3 are like 3x and Sy so that we cannot combine them when adding or subtracting them.

Explanation / Answer

a) 4th root (-8)^4

= (-8)^4/4

= (-8)^1

= -8

so its true

b) a real number has one odd root and two even roots

false

c) we need to restrict the domain of nth root functions if n is even number

true

d) 5^5 = 3125

5th root (3125) = 5

true

e) false

f) f(x) = sqrt ( x - 4)

domain is [ 4 , infinity )

true

g) sqrt (x^2 ) = +- x

false

h) sqrt (-8) / sqrt 2 = 2i

true

i) true

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