Radical 1500
√1500
so, now what?
That's my question, what is it
it is the square root of 1500. That is, it is the number which, when multiplied by itself, equals 1500.
√16 = 4 because 4*4 = 16
√25 = 5 because 5*5 = 25
√1500 is not a rational number, but it is approximately 38.73
38^2 = 1444
39^2 = 1521
So, you can see that √1500 is somewhere in between.
To find the radical of a number, we need to determine its prime factors.
Let's find the prime factors of 1500:
1. Start with the smallest prime number, 2. Divide 1500 by 2: 1500 ÷ 2 = 750.
2. Since 750 is also divisible by 2, divide it again: 750 ÷ 2 = 375.
3. Continue dividing by 2 until we can no longer divide evenly: 375 ÷ 2 = 187.5 (not divisible by 2).
4. Move on to the next prime number, 3. Divide 375 by 3: 375 ÷ 3 = 125.
5. 125 is not divisible by 3, so we continue to the next prime number, 5. Divide 125 by 5: 125 ÷ 5 = 25.
6. 25 is a perfect square, so we can stop here.
7. Write down all the prime factors: 2, 2, 3, 5, 5.
To express the radical of 1500, we group the prime factors into pairs:
√1500 = √(2 * 2 * 3 * 5 * 5)
Simplify the pairs inside the radical:
√(2 * 2 * 5 * 5 * 3) = √(2^2 * 5^2 * 3)
Bring out the pairs as individual factors outside the radical:
2 * 5 * √3 = 10√3
Therefore, the radical of 1500 is 10√3.