Can you rewrite the product as a single square root?
A
a
Rational number
B
b
Irrational number
C
c
Irrational number
D
d
Rational number
Practice makes perfect
a
Any sum or product that is rational can be rewritten as a fraction ab, where a and b are integers. Notice that 9 is a perfect square, which means we can simplify this radical to a number. With this information, we can simplify the expression.
Since we were able to rewrite the expression as a fraction ab where a and b are integers, this is a rational number.
b
The symbol π is a symbol that denotes a decimal number with infinite non-repeating decimals.
Ï€ =3.14159265...
Therefore, if we try to rewrite this sum as a fraction, the numerator will never be an integer. This means this is an irrational number.
c
Any square root where the radicand is not a perfect square, such as 4, 9 or 16, will have infinite non-repeating decimals. Since 11 is not a perfect square, and we cannot rewrite the product, this must be an irrational number.
d
Similar to Part C, we see a square root that is not a perfect square, sqrt(3). However since it is multiplied by a second square root, sqrt(12), we can rewrite this as a single square root and then simplify.
