Simplify. See Example 9.

√3
2
———
1 - √3
2

Question

Simplify. See Example 9.

√3
 2
———
1 - √3
 2

Accepted Answer

Welcome back. Everyone. In this problem, we want to simplify the given expression, the square root of 35 divided by six, all divided by one minus the square of divided by six. For our answer choices, A is 35 plus six multiplied by the skirt of 35 B is 35 minus six, multiplied by the skirt of 35 C is negative plus six, multiplied by the skirt of 35 and D is negative 35 minus six multiplied by the skit of 35. Now, what do we know? Well, we want to simplify our expression and it looks complicated as is, but if we can rewrite all of this as a simpler fraction, then it will be easier to work with. So first, let's try and see how we can do that. So what we have here, we're really seeing the ret of 35 divided by six, divided by one minus the square root of 35 divided by six. So first, it would be best to try and write our ent here as one expression. Now to do that where we have one minus the square root of 35 divided by six. So if we think about it, first common denominator between both are, would be 66 times one or six, multiplied by one is six and six into six goes one time. So the square of 35 multiplied by one is a square of 35. Therefore, I can rewrite it as six minus the square of 35 all divided by six. Let's use what we know about dividing fractions, which means I can rewrite this as a square of 35 divided by six, multiplied by six, divided by six minus the square root of 35. Now both terms have a common factor of six. And when we factor it out, it leaves us with the spirit of 35 multiply it by one which is the skirt of 35 divided by six minus the spirit of 35. Now, we have a single caution to deal with and that makes it easier. Now, how are we going to simplify this? Well, not that we have a radical in our denominator. So to get to, to make our caution simpler, we can try to rationalize the denominator of our rationalizing means that we're going to rewrite it without a radical and we can rationalize a radical difference by multiplying it by its conjugate. No, I recall that the conjugate of a radical difference. So let's say whichever that give them in the form A minus the squared of B then the conjugate would be equal to a value with the same whole number part, which is a but the opposite radical part. So in this case, it would be plus the spirit of B. So that tells us then that the conjugate, the conjugate of six minus the square of 35 equals six plus the squares of 35. And now we can multiply both our numerator and denominator by that conjugate. So we can rewrite our expression as a square of 35 divided by six minus the square of multiplied by the conjugate in the numerator and in the denominator. Now, the reason why we put the conjugate in the denominator is because when we multiply six minus the square of 35 and six plus the square of 35 both of those are the sum and the difference of the same numbers, which means that we can use the difference of two squares because recall that if we are multiplying the sum and the difference of an expression, we can rw write it as the difference between their two squares. So let's apply that idea here. So we have a skirt of 35 multiplied by six plus the skirt of 35 in our numerator. And in our de denominator, we will now have six squared minus the square of 35 all squared. Now, the skirt of 35 multiplied by six is six multiplied by the skirt of 35 we have to leave it as that. And the skirt of 35 multiplied by the skirt of 35 will just give us 35. In our denominator six squared is 36 and the square of 35 squared is six multiplied by the script of 35 plus 35 would still be our numerator. We, we really can't do anything else, but in our denominator 36 minus 35 equals one. So our final answer would be six multiplied by the skirt of plus 35. And when we look in 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. √3 2 ——— 1 - √3 2

Key Concepts

Rationalizing the Denominator

Simplifying Radicals

Combining Like Terms

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