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How do you simplify: square root of x^6*y^6?

Answer 1

Divide the exponent by 2 and this will be the number of variables you can extract from the root.

If you got #sqrt(x^6y^6)#, divide each exponent by the index of the root (in this case, a square root has index 2), we obtain #6/2=3# So we can extract each variable 3 times. You can see it more graphically this way:

#sqrt(x^6y^6)=sqrt(x^2x^2x^2y^2y^2y^2)=x^3y^3#

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Answer 2

Eva Abramson

To simplify the expression √(x^6 * y^6), we can use the properties of exponents and square roots.

First, we can rewrite x^6 * y^6 as (x * y)^6.

Next, we can apply the property of square roots, which states that √(a * b) = √a * √b.

Using this property, we can simplify the expression as √(x * y)^6 = √x^6 * √y^6.

Since the square root of x^6 is x^3 and the square root of y^6 is y^3, the simplified expression is x^3 * y^3.

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Answer 3

Isaiah Anthony

To simplify ( \sqrt{x^6y^6} ), you can apply the properties of exponents and square roots:

Take the square root of each factor separately.
Simplify each factor by halving the exponent.

So, ( \sqrt{x^6y^6} = \sqrt{x^6} \times \sqrt{y^6} = x^{\frac{6}{2}} \times y^{\frac{6}{2}} = x^3y^3 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.