Simplify by factoring
Assume that all expressions under radicals represents non negative numbers
3square root symbol 162x8
I end up with 3x 3squareroot symbol 2x^5
I don't think this is correct help
I will assume you meant
3√(162x^8)
= 3√2√81√x^8
= 27√2 x^4
so the answer is 27 Square root symbol 2x^4
To simplify the expression √162x^8, we can start by breaking down 162 and x^8 into their prime factors. Let's begin with the number 162:
1. Find the prime factors of 162: 2 x 81.
2. Further break down 81: 3 x 27.
3. Continue breaking down 27: 3 x 9.
4. Finally, break down 9: 3 x 3.
So, the prime factorization of 162 becomes 2 x 3 x 3 x 3 x 3.
Next, let's simplify the term x^8:
1. Express x^8 as (x^4)^2.
Now that we have expressed 162 and x^8 in their prime factorizations, we can rewrite the original expression:
√(162x^8) = √(2 x 3 x 3 x 3 x 3 x (x^4)^2)
To simplify the square root, we can bring out pairs of factors from underneath the radical:
= √[(2 x 3 x 3) x (3 x (x^4)^2)]
= 3 x (x^4) √(2 x 3 x 3)
= 3x^4√(18)
Now, we can simplify the square root of 18:
1. Find the prime factors of 18: 2 x 9.
2. Further break down 9: 3 x 3.
The prime factorization of 18 becomes 2 x 3 x 3.
Substituting this back into the expression, we get:
= 3x^4√(2 x 3 x 3)
= 3x^4√(2 x 3^2)
= 3x^4 x 3√2
= 3x^4 x 3√2
= 9x^4√2
Therefore, the simplified expression is 9x^4√2.