In Exercises 33–46, simplify each expression.
_____
−√100x⁶

Question

Accepted Answer

Welcome back. I am so glad you're here. We're told for the given expression, simplify the expression that we're given is the negative square root of 289 X raised to the eighth power. And our answer choices are answer choice A 17 X to the fourth answer. Choice B negative 17 X to the fourth answer choice C 17 X to the eighth and answer choice D negative X to the eighth. All right. When we are finding the square root of anything, what we need to do is have two of whatever factor in order for it to come outside of the radical two. Because the unwritten index here of our radical is two when we're taking the square root. So is there any number multiplied by itself that gives us 289, 289 is 17 multiplied by 17 or in other words, 17 squared. So we can rewrite that inside of the radical. We'll bring down this negative square root of and 289 is 17 squared. Now, for X to the 8th X to the eighth can be broken down so that there is two of something that gives us X to the eighth. That's the same as X race to the fourth power multiplied by X race to the fourth power or X race to the fourth power squared to give us a square in there. So we have negative square root of 17 squared X to the fourth squared. And now anything that's squared gets to come outside of the radical and hang out with this negative here in front. So we have negative 17 as it goes through the radical, it's not squared anymore. And X to the fourth again, it loses that squared. So we've got negative 17 X to the fourth which matches answer choice B well done. We'll catch you on the next one.

In Exercises 33–46, simplify each expression. _____ −√100x⁶

Key Concepts

Square Roots

Properties of Exponents

Simplifying Radical Expressions

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