Find the square of each radical expression. See Example 2. √3x...

Question

Find the square of each radical expression. See Example 2. √3x² + 4

Accepted Answer

Hey, everyone here we are asked to determine the square of the following expression, the square root of 16 X cubed plus nine. Here we have four answer choice options, answer choice A four X multiplied by the square root of X plus three. Answer B 16 xq plus nine, answer C four XQ plus nine and answer D 16 X squared plus three. So the first thing we need to note with this problem is that when we determine the square of this expression, that means we need to take our entire expression and raise it to the power of two. And now the next thing we want to recall is that when we take the square root of some expression, that is the equivalent of raising that expression to the power of one half. So rewriting this expression in that manner, we have the quantity of 16 X cubed plus nine raised to the power of one half. And this whole expression is raised to the power of two. And now we just want to recall the power to a power role for exponents which states that a raise to the power of M and then raise to the power of N is equivalent to a raise to the power of M multiplied by N. So now this tells us that we can take our two exponents here, which is one half and two and multiply them together. So rewriting our expression, we have the quantity of 16 X cubed plus nine raised to the power of one half multiplied by two. Now just simplifying the exponent, we again have the quantity of 16 X cubed plus nine. Now raised to the power of two divided by two. Simplifying the exponent. Once again, we have the quantity of 16 X cubed plus nine raised to the power of one. And now we see the expression is just raised to the power of one which is equivalent to just the expression itself. So our final simplified expression is 16 X cubed plus nine. So now we are left here with answer choice B where we have found that the square of our given expression is 16 X cubed plus nine. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Find the square of each radical expression. See Example 2. √3x² + 4

Key Concepts

Radical Expressions

Squaring a Radical Expression

Algebraic Simplification

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