SOLUTION: These radical expressions confused me, the question requires me to write whether the expression is irrational or rational. "Determine whether each of the following is rational

Algebra ->  Radicals -> SOLUTION: These radical expressions confused me, the question requires me to write whether the expression is irrational or rational. "Determine whether each of the following is rational       Log On


   

Question 1119842: These radical expressions confused me, the question requires me to write whether the expression is irrational or rational.
"Determine whether each of the following is rational or irrational:
a) square root of 2 + square root of 50
b)C=2(pi symbol)r, evaluated for r= n to the power of negative 1"
Thank you!
Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Determine whether each of the following is rational or irrational:
a) square root of 2 + square root of 50
sqrt%282%29+%2B+5%2Asqrt%282%29 = 6%2Asqrt%282%29
:
b)C=2(pi symbol)r, evaluated for r= n to the power of negative 1"
:
Both are irrational
sqrt%282%29 & pi are irrational, so the expressions are irrational

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


(a) sqrt%282%29%2Bsqrt%2850%29+=+sqrt%282%29%2B5%2Asqrt%282%29+=+6%2Asqrt%282%29

The square root of 2 is irrational, so the square root of 2 multiplied by any rational number is still irrational.

6 is a rational number, so this first expression is irrational.

(b) "C=2(pi symbol)r, evaluated for r= n to the power of negative 1"

That is, 2%28pi%29%28n%5E-1%29+=+2%28pi%29%2Fn

Pi is irrational, so pi divided by any rational number is irrational.

However, the statement of the problem does not specify any restrictions on the value of n. If n is any rational multiple of pi, then this expression is rational.

2%28pi%29%2F7 is irrational
2%28pi%29%2F%287%28pi%29%29+=+2%2F7 is rational

So the problem is not defined clearly enough for us to say whether this second expression is rational or irrational.