Hi first of all thank you very much

I have a question its about simplifying radicals

2^3 square root 128x^4 subtract 2x63 square root 54x

can you please

Hi first of all thank you very much

I have a question its about simplifying radicals

2^3 square root 128x^4 subtract 2x63 square root 54x

can you please

Tutors, please sign in to answer this question.

Do you mean 2 ^{3}√(128x^{4}) - 2*6 ^{3}√(54x) ?

It looks like your problem may really involve cube roots, not square roots.

So, this is 2 times the cube root of the whole term (128x^{4}) under the radical minus 2 times the cube root of the whole term (54x) under the radical.

If this is the case, you will want to first simplify each individual radical (cube root)

In order to simplify a cube-root radical, you will want to look for perfect cubes that are factors. Generally, you want to find the largest perfect cube factor. Do you know what a perfect cube is? 8 is a perfect cube because 2*2*2 = 8, or 2^{3} = 8. 27 is a perfect cube because 3*3*3=27, or 3^{3}=27. For simplifying cube-root radicals, it may be best if you know (or have memorized) some perfect cubes. I've already mentioned 2^{3} and 3^{3}. 4^{3}=64 and 5^{3}=125. If you remember at least these 4 perfect cubes, that should help.

Now for the variable part of the terms, you also want to look for perfect cubes. If the variable has an exponent that is a multiple of 3, like 3, 6, or 9, it would be a perfect cube. So, x^{3}, x^{6}, x^{9} are all perfect cubes.

Now, let's look at simplifying the radical expression that you have.

Think: What is the largest perfect cube that is a factor of 128? Well, 64*2 = 128, and 64 IS a perfect cube.

Then, to deal with the variable part of the term, think about the largest perfect cube that is a factor. We can write x^{4} as x^{3}x, since x^{4} is the same as x*x*x*x.

So, the cube root of 128x^{4} can be rewritten as the cube root of 64*2*x^{3}*x. Since 4^{3}=64, the cube root of 64 is 4. Also, the cube root of x^{3} is x.

Thus, the first term 2 ^{3}√(128x^{4}) is the same as 2*
^{3}√(64*2)(x^{3}*x) = 2*(4x) ^{3}√(2x) since the cube root of 64 is 4 and the cube root of x^{3} is x. Then simplifying this term further gives 8x
^{3}√(2x).

Can you simplify the second term by yourself now?

Then, you will want to combine the terms IF they are like terms (have the same variable and radical parts)

Hope this helps.

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