Directions are simplify by combining like terms.
x radiacal 18 -3 radical 8x^2
can someone show me how to do these types of problems. thanks
I cant determine the second term. For the first, I think you meant
x sqrt(18) which reduces to
x sqrt (9*3) or
3x sqrt 3
First remove squares from under the radical sign
x sqrt(18) = x sqrt (9*2) = 3x sqrt 2
and
3 sqrt(8x^2) = 3 sqrt (4*2*x^2)
= 6x sqrt 2
Now combine terms.
x sqrt(18) - 3 sqrt(8x^2)
= sqrt 2*(3x - 6x) = -3x sqrt 2
You can get other possible answers by using the negative square roots. For example
x sqrt(18) = x sqrt (9*2)
= (+ or -) 3x sqrt 2
To simplify expressions involving radicals, you need to follow a few steps. Let's break it down for the given expression:
1. Start by simplifying each term individually by removing perfect square factors from under the radical sign.
- For the first term, x * √18:
- We can simplify the square root of 18 since it can be broken down as the product of a perfect square and another number: 18 = 9 * 2.
- Taking the square root of 9 gives us 3, so we have x * √(9 * 2) = x * (3 * √2) = 3x√2.
- For the second term, -3 * √(8x^2):
- Similarly, we can simplify the square root of 8 and x^2: 8 = 4 * 2 and x^2 is already a perfect square.
- Taking the square root of 4 gives us 2, so we have -3 * (2 * √2 * x) = -6x√2.
2. Now that we have simplified each term, we can combine them.
The expression becomes: 3x√2 - 6x√2.
3. Finally, you can combine like terms by adding or subtracting the coefficients of the radical terms.
In this case, we have 3x√2 - 6x√2, which simplifies to (-3x)√2.
So, the simplified form of the given expression is -3x√2.
Remember that there might be different ways to simplify an expression involving radicals, and depending on the context of the problem, you might consider using positive or negative square root solutions.