+150 When the numbers $\sqrt{2}, \sqrt[3]{3},$ and $\sqrt[5]{5}$ are listed in order from least to greatest, which number is in the middle?
Suppose $a$ and $b$ are positive integers and $\dfrac{a}{4}+\dfrac{b}{3}=\dfrac{13}{12}$. What is the value of $a^2+b^2$?
What is the largest perfect square less than 12345654320?
How many positive integers less than 2000 are of the form $x^n$ for some positive integer $x$ and $n\ge 2?$
I have until next Saturday, so take your time!
+129845 When the numbers \($\sqrt{2}, \sqrt[3]{3},$ and $\sqrt[5]{5}$ \) are listed in order from least to greatest, which number is in the middle?
Compare
√2 3√3 , 5√5 raise each to the 30th power
(2^(1/2))^30 (3^(1/3))^30 (5^(1/5))^30
2^15 3^10 5^6
32768 59049 15625
So
√2 is the middle number
+129845 Suppose a and b are positive integers and \(\dfrac{a}{4}+\dfrac{b}{3}=\dfrac{13}{12}\). What is the value of a^2+b^2?
a/4 + b/3 = 13/12
[ 3a + 4b] 13
_______ = ___
12 12
This implies that 3a + 4b = 13
If we want positive integer values.....then a = 3 and b = 1
So
a^2 + b^2 =
3^2 + 1^2 =
9 + 1 =
10
+150 Thank you so much, c-phil!
Ironically, just as you answered one of the questions, I figured out one of them too.
