Exercises 73–75 will help you prepare for the material covered...

Question

Exercises 73–75 will help you prepare for the material covered in the next section. Simplify: √18 - √8

Accepted Answer

Hello today we're going to be evaluating the square root of 48 minus the square root of 27. So in order to go ahead and evaluate this, we need to first simplify the square root of 48 the square root of 27. So in order to do that, we can go ahead and break up both numbers into a product of prime numbers. So 48 can be rewritten as 12 times 44 can be rewritten as two times two. And both of these are prime numbers. So I'm gonna go ahead and circle those for now. 12 can be rewritten as six times two And six can be rewritten as three times 2. And both of those are prime numbers as well. So we can go ahead and rewrite the square root of 48 as the square root of two times two times two times two times three. And the square root essentially allows us to remove groups of numbers in groups of two. So we have a group of twos here and a group of tools here. And taking this out of the square root is going to give us two times two times the square root of three and two times two gives us four. So the square root of 48 can be rewritten as four square root of three. Now we're gonna go ahead and repeat this process for 27. 27 can be rewritten as nine times three with three being a prime number and nine can be rewritten as three times three with both of those being prime numbers. So the square root of 27 can be rewritten as the square root of three times three times three. And just like before we have a group of threes here, so we can go ahead and take that out. So the square root of 27 can be rewritten as three times the square root of three. Now, all we need to do is just go ahead and put this back into the form of our original equation. So we can rewrite this as four square root of three minus three square root of three and foursquare minus three squared or three is just going to give us one square 23 or just the square root of three. And that's going to be the solution to this problem. And the answer to this problem is going to be a So I hope this video helps you in understanding how to evaluate this type of equation. And I'll go ahead and see you all in the next video.

Exercises 73–75 will help you prepare for the material covered in the next section. Simplify: √18 - √8

Key Concepts

Simplifying Square Roots

Like Radicals

Subtraction of Radicals

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