Perform the operation and/or simplify each of the following. Assume all variables represent positive real numbers. √50

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Hello. Today we're going to be evaluating the given expression. So what we are given is the square root of Now, is not a perfect square. However, what we can go ahead and do is break down 294 into a product of prime numbers. So let's go ahead and do that by using a number tree. We're gonna write down 294 and the first two numbers we're gonna put on our number tree are two numbers that can multiply to give us Two numbers that can multiply to give us 294 is going to be two times 147 And this is where two is going to be a prime number. Now let's break down 147, 147 can be rewritten as seven times and seven is going to be another prime number on this number tree. Next 21 can be rewritten as seven times And seven and 3 are both prime numbers. So we can't break this down any further. So what we have now is two times seven times seven times three and that is going to equal to 294. And if we combine seven times seven, what we get is seven squared times two times three and that is going to equal to 294. So let's go ahead and replace 294 with seven squared times two times three. So doing this is going to leave us with the square root of seven squared times two times three. And what the square root allows us to do is take out any numbers that are in multiples of two. Here we have seven squared which can be simplified by being pulled out of the square root. So if we remove seven squared from the square root, what we are left with is seven times the square root of two times three and two times three cannot be pulled out of the square root because they are not in pairs of two. So what we're going to do is just multiply two and three together. Two times three is going to give us six. So that's gonna leave us with seven times the square root of six. And this is going to be the simplified form of the given square root. And with that being said, the answer to this problem is going to be be So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video

Perform the operation and/or simplify each of the following. Assume all variables represent positive real numbers. √50

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Key Concepts

Square Roots

Simplifying Radicals

Properties of Exponents