Ok, I have a problem with this, I know how to do what it's asking, but I don't know how to find n.
The problem is:
Suppose that in standard factored form a = p1^e1 * p2^e2 ...* pk^ek, where k is a positive integer; p1, p2,...,pk are prime numbers; and e1, e2,...,ek, are positive integers.
a) What is the standerd factored form for a^2?
I know the answer to this is p1^2*e1 * p2^2*e2... * pk^2*ek.
b) Find the least posivtive integer n such that 2^5 * 3 * 5^2 * 7^3 * n is a perfect square. Write the resulting product as a perfect square.
n = 42, 2^5 * 3 * 5^2 * 7^3 * n = 5880^2
The answer to this is in the back of the book, it makes sense and I see how and why they got it, but I don't understand how they got the n as 42 in the problem, it is not stated in the question and I don't know how you find it. The back of the book just has what I put as the answer printed as is, no explanation how to solve for n, nor is there any examples on the book to do this.
Please, somebody help me.
The problem is:
Suppose that in standard factored form a = p1^e1 * p2^e2 ...* pk^ek, where k is a positive integer; p1, p2,...,pk are prime numbers; and e1, e2,...,ek, are positive integers.
a) What is the standerd factored form for a^2?
I know the answer to this is p1^2*e1 * p2^2*e2... * pk^2*ek.
b) Find the least posivtive integer n such that 2^5 * 3 * 5^2 * 7^3 * n is a perfect square. Write the resulting product as a perfect square.
n = 42, 2^5 * 3 * 5^2 * 7^3 * n = 5880^2
The answer to this is in the back of the book, it makes sense and I see how and why they got it, but I don't understand how they got the n as 42 in the problem, it is not stated in the question and I don't know how you find it. The back of the book just has what I put as the answer printed as is, no explanation how to solve for n, nor is there any examples on the book to do this.
Please, somebody help me.