Order the following sets of numbers from least to greatest:
250^0, √525, (7^2-1)
To order the sets of numbers from least to greatest, we need to simplify each expression first.
1) Simplify 250^0:
Any number raised to the power of zero is equal to 1.
Therefore, 250^0 = 1.
2) Simplify √525:
Prime factorize 525:
525 = 3 * 5 * 5 * 7 = 3 * 5^2 * 7
Take the square root of 525:
√525 = √(3 * 5^2 * 7)
The square root of 5^2 is 5, so we can simplify further:
√525 = √(3 * 25 * 7) = √(3 * 5^2 * 7) = 5√(3 * 7) = 5√(21)
3) Simplify (7^2 - 1):
(7^2 - 1) = (49 - 1) = 48
Now that we have simplified each expression, we can order them from least to greatest:
1, 5√21, 48