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Mathematics
Abbey Burgess
15 July, 04:37
Show ALL work possible
The square root of 72x^5y^12
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Giovani Vazquez
15 July, 08:05
0
When thinking of exponents, you can always write them in the form
x ^ (raise / root)
So, if you are raising x to a power and also taking a root of it, you can write it like a fraction instead!
Lets look at each term!
75 is raised to the first power and we are taking the square (2) root. So, we can write it as
75^ (1/2)
If we think of square factors of 75, we know that 75 = 25*3. Thus, we can write this as
75^ (1/2) = (25*3) ^ (1/2) = 25^ (1/2) * 3^ (1/2) = 5 * 3^ (1/2) = 5 sqrt (3)
x is raised to the fifth power and we are taking the square (2) root. So, we can write it as
x^ (5/2)
This can be simplified. Lets write this as
x^ (4/2 + 1/2) = x^ (4/2) * x^ (1/2) = x^2 * x^ (1/2) = x^2 sqrt (x)
y is raised to the 12th power and we are taking the square (2) root. So, we can write it as
y^ (12/2)
This fraction can be simplified to
y^ (6/1) = y^6
Combining this all together, we get:
5x^2y^6 sqrt (3x)
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