To determine which expression is rational, we need to check if the square root terms can be simplified to rational numbers.
Given:
P = √7
q = √9 = √(3^2) = 3 (since the square root of a perfect square is rational)
r = √2
a) Pq = √7 * 3 = 3√7
b) qr = 3 * √2 = 3√2
c) xp = √7 * √14 = √(7 * 14) = √98
d) Pqr = √7 * 3 * √2 = 3√(7 * 2) = 3√14
Now, we need to determine which expressions have a square root that cannot be simplified further. A rational number is a number that can be expressed as a fraction (p/q) where both p and q are integers and q is not zero.
From the expressions:
P = √7 is irrational since √7 cannot be further simplified into a rational number.
q = √9 = 3 is rational since it can be expressed as 3/1.
r = √2 is irrational since √2 cannot be further simplified into a rational number.
So, the rational expressions are b) qr = 3√2 and d) Pqr = 3√14.
Answers & Comments
Answer:
To determine which expression is rational, we need to check if the square root terms can be simplified to rational numbers.
Given:
P = √7
q = √9 = √(3^2) = 3 (since the square root of a perfect square is rational)
r = √2
a) Pq = √7 * 3 = 3√7
b) qr = 3 * √2 = 3√2
c) xp = √7 * √14 = √(7 * 14) = √98
d) Pqr = √7 * 3 * √2 = 3√(7 * 2) = 3√14
Now, we need to determine which expressions have a square root that cannot be simplified further. A rational number is a number that can be expressed as a fraction (p/q) where both p and q are integers and q is not zero.
From the expressions:
P = √7 is irrational since √7 cannot be further simplified into a rational number.
q = √9 = 3 is rational since it can be expressed as 3/1.
r = √2 is irrational since √2 cannot be further simplified into a rational number.
So, the rational expressions are b) qr = 3√2 and d) Pqr = 3√14.
The correct answer is:
b) qr
d) Pqr