Which of the following results in a sum or a product that is rational? Choose all that apply
A.4+9
B.PI*5
C.3.45*1.2
D.sqrd16*sqrd4
E.sqrd7*sqrd2
sqrd=square root. the 3.45 has a line over the 45 I didn't know how to do that on here.
any number with pi in it is not rational.
any number with sqrt 7 in it or sqrt 2 in it is not rational
all the others can be expressed as a ratio of whole numbers.
13/1
3.454545454545.....
= 3 + 45/100 + 45/10,000 + 45/ 1,000,000 etc
= 3 + 45/100 + 1/100 (45/100)+ 1/100^2 (45/100)
geometric series a=45/100, r = 1/100
see http://www.mathsisfun.com/algebra/sequences-sums-geometric.html
sum = a (1/(1-r)) = 45/100(1/.99)
= 45/99
so
3.454545.... = 3 + 45/99 = 342/99
4 * 2 / 1
I told you all but B and E
Make sure you understand C, how to express a repeating decimal as a ratio of whole numbers (rational) using infinite geometric sequence.
ok thanks Damon
Well, aren't we feeling mathematically inclined today? Let's break this down with a touch of humor!
A. 4 + 9: This one is a piece of cake! The sum of 4 and 9 is definitely rational. No funny business here.
B. PI * 5: Uh-oh, we've got a wild pi in the equation! When multiplied by 5, we get a result that is irrational. It's like trying to put a bowtie on a pineapple – it just doesn't make sense!
C. 3.45 * 1.2: Ah, a decimal multiplication dance! Don't worry, this one stays in the realm of rational numbers. No irrational shenanigans here.
D. sqrd16 * sqrd4: Raise those math shields, because we're battling with square roots! In this case, the square root of 16 is 4, and the square root of 4 is 2. When multiplied together, we're left with 4 * 2, which is definitely rational. Phew!
E. sqrd7 * sqrd2: Oh, those rowdy square roots are at it again! The square root of 7 is a bit of an irrational rascal, and the square root of 2 is no different. When multiplied together, we end up with an irrational product. It's like mixing a clown with a mime – the result won't make any sense!
So, recap time! The options that result in a sum or product that is rational are A (4 + 9), C (3.45 * 1.2), and D (sqrd16 * sqrd4). No funny business with pi or that wild square root party for these ones!
To determine which options result in a sum or a product that is rational, let's analyze each option:
A. 4 + 9
The sum of 4 and 9 is 13, which is a rational number.
Conclusion: This option results in a rational sum.
B. PI * 5
The product of PI (π) and 5 is an irrational number since π is irrational.
Conclusion: This option does not result in a rational product.
C. 3.45 * 1.2
To multiply these decimal numbers, we don't need to worry about the line over the 45 since it indicates the repeating decimal pattern, which does not affect the rationality of the result. The product of 3.45 and 1.2 is 4.14, which is a rational number.
Conclusion: This option results in a rational product.
D. sqrd16 * sqrd4
The square root of 16 is 4, and the square root of 4 is 2. Therefore, the product of the square root of 16 and the square root of 4 is 4 * 2 = 8, which is a rational number.
Conclusion: This option results in a rational product.
E. sqrd7 * sqrd2
The square root of 7 is an irrational number since 7 is not a perfect square. The square root of 2 is also irrational. Therefore, the product of these two irrational numbers is irrational.
Conclusion: This option does not result in a rational product.
To summarize, the options that result in a sum or a product that is rational are:
A. 4 + 9
C. 3.45 * 1.2
D. sqrd16 * sqrd4