How do i rationalize the denominator of 3m / (2 + sqrt5)?

Answer 1

Rationalizing the denominator

3m/2 √5

3m √5/2 √5 √5

3m √5 /2 √25

3m √5 / 2 x 5

3m √5 / 10

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Method 2

3m / 2 √5

3m 2 √5 / 2 √5 2 √5

6m √5 / 4 √25

3m √5 / 2 x 5

The numerator and denominator simplify to 3m √5 / 2 x 5

3m √5 / 10

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Answer 2

The above poster answered the question based off the way you worded the question. But somehow, I believe that you really meant "6/(sqrt5 +2) If that's the case, the solution you want begings with multiplying both the numerator and denominator by the conjugate of sqrt5 + 2, which is sqrt5 -2. This yields 6(sqrt5 - 2) in the numerator. In the denominator, you can simplify to get 5 - 4, which is 1. So the answer based off what I *think* you meant, is 6(sqrt5 -2) or 6sqrt5 - 12

Answer 3

Multiply the numerator and demoninator by the conjugate (2-sqrt5)
[3m*(2+sqrt5)]/[(2+sqrt5)*(2-sqrt5)]

6m+3(sqrt5)m/(4-2sqrt5+2sqrt5-sqrt25)
6m+3(sqrt5)m/(4-5)
6m+3(sqrt5)m/(-1)
-6m+-3(sqrt5)m

Answer 4

it's so simple, just use the general rationalising method sweety, ur will get a correct answer.

Answer 5

yes you do