how do i find the square root of 50x^10
x^5 sqrt (2*25)
5 x^5 sqrt 2
To find the square root of 50x^10, we can break down the problem into smaller steps. Here's how you can approach it:
Step 1: Simplify the expression.
The square root of 50 can be simplified as the square root of 25 times the square root of 2. Similarly, x^10 can be simplified as x^5 times x^5. So, we can rewrite the expression as:
√(25 * 2 * x^5 * x^5)
Step 2: Simplify further.
The square root of 25 is 5, and since it is a perfect square, it can be taken out of the square root. We'll also simplify the x terms:
5 * x^5 * √(2 * x^5)
Step 3: Combine like terms.
Since both x terms have the same exponent of 5, we can combine them:
5 * x^(5 + 5) * √2
Step 4: Simplify the exponent.
The exponent of x in step 3 simplifies to:
5 * x^10 * √2
So, the square root of 50x^10 simplifies to:
5x^10√2
To find the square root of 50x^10, you can follow these steps:
Step 1: Simplify the expression inside the square root.
50x^10 can be rewritten as 25 * 2x^10.
Step 2: Split the expression into two separate square roots.
√(25) will give you 5, and √(2x^10) will be left as is.
Step 3: Simplify the remaining square root.
Break down the expression √(2x^10) into separate square roots: √(2) * √(x^10).
Step 4: Simplify √(x^10).
Since x^10 can be written as (x^5)^2, we have: √(x^5)^2.
Step 5: Remove the square and simplify.
The square root and square will cancel out for x^5, resulting in x^5.
In conclusion, the square root of 50x^10 is 5x^5.