Squaring off. Let S stand for the set of all natural numbers that are perfect squares, so S = {1, 4, 9, 16, 25, 36, 49, 64, . . . }. Show that the set S and the set of all natural numbers have the same cardinality by describing an explicit one-to-one correspondence between the two sets.

45

step-by-step explanation:

d. 8

step-by-step explanation:

the given radical expression is:

we can rewrite this as:

we express as square numbers to get;

the exponents will now cancel out to give.

the correct answer is d

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b