Perform the indicated operations and/or simplify each expressi...

Question

Perform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. ∜2/25

Accepted Answer

Welcome back. I am so glad you're here. We are given this expression, we're taking the fourth rut of a fraction in the numerator we have three. And in the denominator we have 49. We need to rationalize this, we need to simplify it so that there is no radical in the denominator, no radicals allowed in the denominator. Alright, so we recall from previous lessons that we can rewrite this due to the quotient rule of radicals by taking the fourth rut Of our numerator. So the fourth root of three over the four threat of our denominator. So the fourth threat of 49. And now we need to focus on getting that outside of the fourth root. How do we do that? Well in order to come out of a radical with 1/4 root there has to be four of any factor. We know that 49 is already seven times seven. So we just need two more sevens in order to get a seven out of there. And so we can multiply This times the four threat Of another 49. So that's another seven times seven. What we do to the denominator we need to do to the numerator as well. Multiply this by the four threat of 49 as well. So now just doing that multiplication in the numerator, we have the four threat of three times 49. And in the denominator we have the four threat of 49 squared. I'll just write this as seven times seven times seven times seven. So we know that we'll be able to pull a seven out of there. So let's go ahead and do that in the denominator. The four threat of seven to the fourth power is seven In the numerator. We just have a three times a seven times a seven. There aren't four of any factor so we can multiply three times 49. So we have the four threat of three times 49 which is 147. And that doesn't simplify any further. So this is our final answer looks like I said not equal to their the fourth threat of divided by seven. We look at our answer choices and this matches with answer choice. D. Well done. We'll catch you on the next one.

Perform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. ∜2/25

Key Concepts

Radical Expressions and Roots

Properties of Exponents and Radicals

Simplification of Radical Expressions

Watch next