Evaluate each expression or indicate that the root is not a re...

Question

Evaluate each expression or indicate that the root is not a real number.

$\frac{\sqrt7}{\sqrt3}$

Accepted Answer

Hello, today we are going to be rationalizing the denominator of the given radical expression. The radical expression given to us is the square root of 31 divided by the square root of 91. Now, what does it mean to rationalize the denominator? Well, in order to rationalize the denominator, we want to rewrite the denominator in a form that does not contain the square root symbol. So how can we go about doing this? We recall that the square root symbol allows us to simplify perfect squares into its base term. So if we have the square root of 91 what is the quantity that we can multiply to this? To give us the square root of 91 squared? What what we could do is we can multiply this denominator by the square root of 91. The product of these square roots together will allow us to eliminate the radical sign in the denominator. But we need to be careful because if we multiply the denominator by the square root of 91 we must also do the same in the numerator. So now what we need to do is we need to multiply the numerators and denominators together in the numerator square root of 31 multiplied by the square root of 91 will leave us with the square root of 2821. In the denominator, we will have the square root of 91 multiplied by the square root of 91 which will leave us with the square root of 91 squared. We can then simplify the denominator to just be 91. So what we are left with is the square root of 2821 divided by 91. This is going to be the simplified form of the given radical expression with a rationalized denominator. And with that being said, the answer to this problem is going to be c 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.

Evaluate each expression or indicate that the root is not a real number.
$\frac{\sqrt7}{\sqrt3}$

Key Concepts

Square Roots

Rationalizing the Denominator

Real Numbers

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