Express in simplest radical form.x, squared, square root of, x, to the power 9 , end square rootx 2 x 9
Question
Express in simplest radical form.x, squared, square root of, x, to the power 9 , end square rootx 2 x 9
Solution 1
The expression you provided seems to be a bit unclear. However, if you're asking to simplify the square root of x to the power of 9, here's how you can do it:
Step 1: Write down the expression √(x^9)
Step 2: Break down the exponent inside the square root into a multiple of 2 (since we're dealing with a square root) and keep the remainder (if any). In this case, 9 = 2*4 + 1.
So, we can write x^9 as (x^8) * (x^1).
Step 3: Simplify the square root using the rule √(a*b) = √a * √b.
So, √(x^9) = √(x^8) * √(x^1).
Step 4: Simplify further. The square root of x^8 is x^4 (since (x^4)^2 = x^8). The square root of x^1 is just √x.
So, √(x^9) = x^4 * √x.
So, the simplest radical form of √(x^9) is x^4√x.
Solution 2
The expression you provided seems to be a bit unclear, but if you're asking to simplify the square root of x to the power of 9, here's how you can do it:
Step 1: Write down the expression √(x^9)
Step 2: Break down the exponent inside the square root into a multiple of 2 (since we're dealing with a square root) and keep the remainder. In this case, 9 = 2*4 + 1. So, we can write x^9 as (x^8 * x^1)
Step 3: Now, take the square root: √(x^8 * x^1) = √(x^8) * √(x^1)
Step 4: Simplify the square roots. The square root of x^8 is x^4 (since 42 = 8) and the square root of x^1 is just x (since 12 = 2). So, √(x^8) * √(x^1) = x^4 * x
Step 5: Combine the results to get the final answer: x^4 * x = x^(4+1) = x^5
So, the square root of x to the power of 9 in simplest radical form is x^5.
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