Express the radical as a power. Then evaluate it. Round to the hundredths place. I can't figure out how to type the symbols on my computer, but there are 3 problems. 1) 795 "square-rooted to the 3rd power" 2) 9876 "square-rooted to the 5th power" 3) 845.3 "square-rooted to the 7th power" I hope that makes sense.
<<I hope that makes sense.>>
It doesn't.
To express a radical as a power, you can use the exponent property of radicals. The general exponent property states that for any positive integer n and any positive real number a, the nth root of a raised to the nth power is equal to a.
To apply the exponent property to these problems, you need to calculate the nth root first, and then raise that result to the nth power.
Let's go through each problem step by step:
1) 795 "square-rooted to the 3rd power":
First, find the cube root of 795. You can use a calculator to do this. Let's assume the cube root of 795 is approximately 9.945.
Next, raise the cube root to the 3rd power: 9.945^3 ≈ 985.56.
Round this result to the hundredths place: 985.56 rounded to the hundredths place is 985.56.
So, 795 square-rooted to the 3rd power is approximately 985.56.
2) 9876 "square-rooted to the 5th power":
Similarly, find the fifth root of 9876. Let's say the fifth root of 9876 is approximately 6.728.
To get the value when raised to the 5th power: 6.728^5 ≈ 211,014.08.
Rounding this result to the hundredths place gives you 211,014.08.
Therefore, 9876 square-rooted to the 5th power is approximately 211,014.08.
3) 845.3 "square-rooted to the 7th power":
Find the seventh root of 845.3, which is approximately 1.748.
Raise this result to the 7th power: 1.748^7 ≈ 48.56.
Rounding this result to the hundredths place gives you 48.56.
Thus, 845.3 square-rooted to the 7th power is approximately 48.56.