Simplify the square root 48x^4?

Question

I keep confusing simplify and evaluate can someone please help and give me an explanation that may help me understand the difference better

Answer 1

Simplify means to perform algebraic manipulations in order to change the look of the numbers and variables. x+x gets simplified to 2x. Eventually you will find that simplest form is kind of based on opinion. It generally means do all the addition, subtraction, multiplication, division, and combining like terms that you can.

Evaluate is more like calculate. Evaluate can also mean they have given you an expression such as 3x+5 AND give you a value for x such as x=7. Then you plug that number into the expression 3(7)+5 which calculates to 26.

Simplifying usually ends up with letters and numbers. Evaluating should always end up with only a number.

Good question.

Answer 2

You can only evaluate when there is an equals sign because evaluate means to find what the variable equals. If there is no equal sign, then you can't find what the variable equals.
Simplifying just means to break down what is given.

I always remember E and E: evaluate and equal sign.

Now, root(48x^4).

You need to simplify because there are perfect squares inside the radical.

First, look at the 48. You need to know your perfect squares, up to 48. They are 4, 9, 16, 25, and 36. Well, obviously 25 and 36 will not work.

How about 16? Yes. 16(3) = 48

root[ 16(3)x^4]

Now, you can pull out the 16 and take the square root of it... and put it outside the radical.

4root(3x^4)

Now, let's look at the x^4. Think about it. When you raise a power to a power, you multiply exponents. Square root is the same as raising something to the 1/2 power. So, what's (x^4)^(1/2)? Correct. You just multiply the exponents. What's 4 and 0.5? Yes, it's 2.

So, you can pull out the whole x^4 and it becomes x^2 outside the radical.

4x^2root(3)

That's your answer. There is no equals sign, so you cannot do anything else with it. ;-)

Oh, and as a side note, if it were the cube root, that's the same as the power of 1/3. The fourth root is the same as the power of 1/4. The reason is because when you raise something to a fractional power, first you raise it to the power of the numerator, and then you take the denominator root of the number you get. You should see the connection.

Good luck.

Answer 3

Simplify Square Root 48

Answer 4

Evaluate means "work out"
Simplify means to cancel and collect similar terms where possible.
√(48x^4) = √(16 x 3) x² = 4√3 x²

Answer 5

Simplify means that you leave the result in terms of square root functions. Evaluate means that you provide the rounded decimal equivalent.

sqrt(48x^4) = sqrt(16)*sqrt(3)*sqrt(x^4) = 4*sqrt(3)*x^2

We leave sqrt(3) in that form because it's an exact value and cannot be simplified further.

Answer 6

We can break it out thusly:

sqrt(48x^4) = sqrt(48)sqrt(x^4)
= sqrt(48)x^2
= sqrt(16)sqrt(3)x^2
= 4sqrt(3)x^2

Answer 7

sqrt(48x^4)= x^2 * sqrt(48) = 4x^2 * sqrt(3):
sqrt (x^4) = x^2, this is as simple as you can have it.
sqrt(48) = sqrt(16)*sqrt(3) = 4 * sqrt(3).
put them all together.

Answer 8

4x^2 * 3^0.5