Simplify √12x^4? Thanks. Step by step description please?

√(12x^4)
= √(2^2 * 3 * x^4)
= √(2^2) * √3 * √(x^4)
= 2 * √3 * x^(4/2)
= 2x^2√3

√x^4 = x^2
12 = 4 * 3 ..... so √ 12 = √ 4*3 = 2√3

√12x^4 = 2 x^2 √3

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First of all you have to express the question properly.
As given, question MUST be read as :-

( √12 ) x^4 = 2√3 ( x^4 )

However I suspect that what you actually mean is :-

√ ( 12 x^4 ) which then becomes

2√3 x ²


PS
Take care with presentation of questions.

Ok so when you are simplifying you are basically taking things within the square root and putting them outside. When you do this, you have to take the square root of the thing you are removing....

1. 12 = 3 x 4, so write (3 x 4) instead of 12: √3 x 4 x x^4

2. the square root of 4 is 2, so when you bring the 4 outside the square root, you write a 2 there: 2√3x^4

3. x^4 is the same thing as x^2 times x^2, so like the last step, when you "bring it outside the square root," the x^4 becomes x^2:

Now you have 2x^2√3

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Another way to think about it:

Anything that has 2 copies underneath a square becomes 1 when you remove it:

You could simplify the whole expression at the beginning to see which ones have pairs:

√(3) x (2) x (2) x (x^2) x (x^2)

There is a pair of 2's and a pair of x^2's:

2x^2√3

√12x^4

From here, we can see that we have an entity that is raised to 4, which is a perfect square. Therefore, we can get its square root, and get:

x^2 √12

12 is not a perfect square, but it is a product of 3 and 4, which is a perfect square. Getting the square root of 4 and leaving 3 inside the radical, we get:

2x^2 √3

That's the final answer.

=(12x^4)^1/2=[(2^2)(3)(x^4)]^1/2=2x^2\/''3'''

√12x^4
√(3*2*2)(x*x*x*x)
2x^2√3

so basically √ means find a pair and bring them out of √.

So in this problem √9x^2 answer is 3x.
In this problem, √100x^5 is 10x^2√x