Help with simplifying radicals?

Question

What are the steps to simplifying:

3 sq.root 3/ 6


Is sqrt3/ 2 right?

Answer 1

Yes. You divided the 3 into the 6, right on!

Answer 2

If you mean (3 √3) / 6, then yes, your answer is correct. It can also be rewritten this way:

(3/6) √3, which is equivalent to (1 / 2) √3 or √3 / 2.

If you mean 3 [√(3 / 6)], then that's an entirely different story. √(3 / 6) is the same thing as √(1 / 2), because 3 / 6 = 1 / 2. √(1 / 2) is equivalent to √1 / √2 = 1 / √2. We then should rationalize the denominator of the last expression, because radicals are not usually left in the denominator of a fraction. We can do that by simply multiplying the numerator and denominator by the denominator. That squares the denominator and puts the radical in the numerator instead. Here's what I mean:

(1 / √2)(√2 / √2) = (1 x √2) / (√2 x √2) = √2 / (√2)² = √2 / 2.

Now we simply multiply the last result by 3, since your original expression was 3 [√(3 / 6)], to get:

3 (√2 / 2) = (3 √2) / 2 or (3 / 2) √2

which as you can see, is not at all the answer for the other case.

Answer 3

3*√(3/6)...

simplify under the root sign to get √(1/2)
but sqrt of 1 is 1, so you end up with


3/√(2)

but we aren't allowed to leave a root in the denominator of a fraction, so multiply the whole thing by √(2)/√(2) ... which is equal to 1 so it will not change the value of the fraction.

3/s√(2) * √(2)/√(2)

tops times tops and bottoms times bottoms
(remember (√2)(√2) = 2)

3√2/2