math exlpaination question?

Question

explain in the word what this is saying
It can be proven that the sq.rt of x*y = Sq.rt X * sq.rt. Y
help me

Answer 1

sq.rt of x*y = Sq.rt X * sq.rt. Y

It can be proven that:
√(x*y) = √x * √y

Consider the first part → √(x*y).
Two number values, one is x and the other is y, they are multiplied together. You then take the square root of this result.

Consider the second part → √x * √y.
You take the square root of x and y and then you multiply the results together.
It can be shown that the results of the first part is the same as the result of the second part.

Answer 2

Basically, this is saying that the square root of product of two factors can be rewritten as the square root of one of the factors times the square root of the other factor. This is useful when the square root gives an irrational number, but the equation can be rewritten in other forms:

sqrt(300) = sqrt(100) * sqrt(3) = 10 * sqrt(3)

If you know the square root of 3 (1.732...), then you can approximate the answer without a calculator:

sqrt(300) = 17.32...

This is also useful when you need to simplify a quotient. For example:

sqrt(27) / sqrt(3) = (sqrt(9) * sqrt(3)) / sqrt(3)

You can now cancel out the sqrt(3) on top and bottom and simplify the sqrt(9)

sqrt(27) / sqrt(3) = 3

Answer 3

It means, if you take the square root of the product of two numbers, you can either multiply them first and then do the square root of the answer, or do the square root of each number first and then multiply these answers.

Sqrt (9x4) = sqrt(36) = 6, or sqrt(9) x sqrt(4) = 3x2 = 6

Answer 4

Let square root of a number n be n^.5 where .5 is the square root. Then (x*y)^.5=(x^.5)(y^.5) ie the distributive power.

Answer 5

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