Simplify. See Example 9.

√7
5
———
√3
10

Question

Simplify. See Example 9.

√7
 5
———
 √3
 10

Accepted Answer

Welcome back. Everyone in this problem. We want to simplify the expression of the spirit of 13 divided by nine all divided by the square of two divided by 18. For our answer choices, A is the ret of 26 B is a skirt of 13 C is the square root of open parenthesis. 13 divided by two, close parentheses and D is open parenthesis, the square root of 13, close parentheses divided by two. Now, what do we want to do here? We want to simplify the expression. But before we do that, let's try and make it look simpler because it's complicated as is. So what we're really doing here is dividing the skirt of 13 divided by nine by the square root of two divided by 18 using what we know about fractions. We can rewrite that as the square of 13 divided by nine multiplied by 18, divided by the square root of two. Notice both terms have nine as a common factor. And when we factor out nine, 9 to 9 goes one time, 9 to 18 goes two times. So that leaves us with two multiplied by the square of divided by the square root of two. No, we have one caution, but it's still not in its simplest form because we have a radical in the denominator. So to get rid of the radical, we can rationalize our denominator. In other words, we need to think of something that we can multiply the square root of to get rid of the radical. The best thing in this case would have been the squared of two. But if we multiply our denominator by the square of two, we will also have to multiply our numerator by the same value. No two multiplied by the square root of 13, multiplied by the square of two will be divided by the skirt of two, multiplied by the skirt of two, which would have been equal to two. Now notice both the numerator and denominator have a common factor of two. And when we factor that out, we are left with the square root of 13 multiplied by the square of two. But what we know here, well, again, recall the product tool of radicals which tells us that if we're finding the radical of a product, it equals the radical of one term multiplied by the radical of the other. So we can apply that property to help us here because that tells us that the skirt of 13 multiplied by the skirt of two would be the same thing as the skirt of 13 multiplied by two, which is the square root of 26. There are no square factors of 26. Therefore, this is our answer in its simplest form. And when we look back on our answer choices, that would have been answer choice. A thanks a lot for watching everyone. I hope this video helped.

Simplify. See Example 9. √7 5 ——— √3 10

Key Concepts

Rationalizing the Denominator

Simplifying Radicals

Fraction Operations

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