Question

Alg1 S1-3 USA OL FY21

Question: 1-15
Ifp and q are non-zero rational numbers, and s and t are irrational numbers, select all of the statements that are always false.
The product pq is irrational.
The product pt is irrational.
The quotient
is irrational
0 The product st is irrational.
The quotient is rational.
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Answer 1

The product st is irrational.

The product pt is irrational.

Explanation:

Let p = 3/4 and q= 5/9

Now multiplying these two non zero rational numbers

3/4 (5/9)= 15/36 ( this is also a rational number)

An irrational number is one which cannot be expressed in the form of p/q where p and q are integers( in the form of a simple expression) like the rational number.

Now let the two irrational numbers s and t be √3 and √5

Now multiplying the two irrational numbers we get

st = √3 √5

st =√15 ( this is also an irrational number)

√15 cannot be expressed in the form of a simple fraction.

Now multiplying pt

3/4 * √5= 3√5/4 ( this is also irrational)