rationalize each denominator........?

Question

1/√2

√2/3

1/7-√6

Answer 1

1/√2 --- multiply top and bottom by √2 to get √2/2

√2/3 --- This is ok... unless you meant it to be √(2/3). In that case, you have √2/√3 and you can multiply top and bottom by √3 to get √6/3

I assume the third one is meant to read 1/(7 - √6). To rationalize the denominator, you need to multiply the top and bottom by the conjugate of 7 - √6 which is 7 + √6

On top, you will have 7 + √6
On the bottom you will have (7 - √6)(7 + √6) = 49 - (√6)^2 = 49 - 6 = 43. (The middle terms drop out because it is a difference of squares... try using FOIL to multiply it out and you'll see what I mean.)

So it is (7-√6)/43

Answer 2

Okay, I will help with the first.

1 / √2

Multiply the denominator times the numerator and denominator, like this:

1(√2) / [(√2)(√2)]

You should know that the square root of any number times the square root of that same number equals that number.

√2 / 2

There you go.

Answer 3

If by these you mean

1/(sqrt(2)) = (sqrt(2))/2

sqrt(2/3) = (sqrt(2))/(sqrt(3)) = (sqrt(6))/3

1/(7 - sqrt(6)) = (7 + sqrt(6))/((7 - sqrt(6)(7 + sqrt(6))) = (7 + sqrt(6))/(49 - 6) = (7 + sqrt(6))/43

Answer 4

(radical 2)/2

The second one has a rational denominator.

(1-7radical6)/7

Any questions? Add them in details

Answer 5

1/sqrt(2) = sqrt(2)/2
Sqrt(2)/3 already done

1/(7-sqrt(6)) = (7+sqrt(6))/(7*7-6) or (7+sqrt(6)/43

Answer 6

Homework causing you problems? Brain not functioning?