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.