1THANK YOU VERY MUCH !!!
HEY,
PLEASE SOLVE THIS PROBLEM:
Todd's bike has a combination lock. To unlock his bike Todd has a secret number that is greater than 100 but less than 1000.
Todd's secret number is a square number and the cube root of his secret number is also a square number.
What is Todd's number??
PLEASE ANSWER SOON !!
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3 Answers
106as the secret no. is a sq no betn 100 and 1000
then it can be 121,144,169,...,312
it is given that its cube root is an integer,
so it can be 125, 216, 343, 512, 729
among these the nos that are common are:
729.
It suffices to see that cube root of 729 is 9 which is also a square no.
So his no. is 729
1Suppose the number is s. It is given that its cube root is a square of an integer.let it be i.
so, √3√s = i;
or. i6 = s;
it is clear that i ≠1,2,4 {as 16,26<100 and 46>1000)
so i = 3;
therefore s = 36 = 729