In Exercises 33–46, simplify each expression.____√36x⁴

Question

Accepted Answer

Hey, everyone in this video, we're gonna be working through the following problem for the given expression, simplify the expression we're given is the square root of 144 x to the exponent four. We have four answer choices. Option A 12 X squared. Option B 144 x squared. Option C negative 12 X squared and option D negative 144 X squared. Let's start by writing what we were given. So we have the square root of 144 x to the exponent four. Now let's notice we can write this as the square root of 12 x squared quipped A, we had 100 44 X to the exponent four. This is equal to 12 X squared. All squared. A 12 squared gives us to the 144 X squared squared can recall if we have an exponent raised to an exponent, we multiply the two exponents together. And so we have X squared squared gives us X to the exponent four. Now we have the square root of something squared. Recall that if we have the nth root of A to the exponent N, we can write this as the absolute value of A, as long as N is, even in our case, we have N is two, OK. We have the square root and something squared. So N is equal to two, we can go ahead and apply this rule and it's even. And so the square root of 12 X squared, all squared is equal to the absolute value of 12 x squared. Now we can simplify a little further and we know that 12 is positive. So it can come outside of our absolute value. We also know that X squared is going to be positive, right? A number multiplied by itself is always gonna be positive. Whether that number is negative or positive. If you multiply two negatives together, you get a positive value. If you multiply two positive values together, you get a positive value. And so both of these values are going to be positive, which means that the absolute value is just going to be equal to 12 X squared. So now we have our simplified expression, we found that the square root of 144 X to the exponent four is equal to 12 X squared, which corresponds with answer choice. A thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 33–46, simplify each expression.____√36x⁴

Key Concepts

Square Roots

Properties of Exponents

Simplifying Radicals

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