Multiplying radicals......please help?

Question

My lesson says if you multiply a radical by itself the answer is the radicand. So the square root of 3 times the square root of three = three. But is 2 times the square root of three the same thing? Or six? Or what? I don't understand that because the 2 isn't a radical, its a plain 2.

Actually the entire problem is: Rationalize the denominator of 2 over the square root of 3. So I multiply both by square root of three, but not sure of how to do the top.

Thanx...

Answer 1

2 / sqrt(3) multiplied by sqrt(3) / sqrt (3)

notice you are mult. by a form of the number one!

2*sqrt(3) / sqrt(3)*sqrt(3)

you cannot combine rational #s like 2 and sqrt(3) so continue to show them as a product the same way you show the product of 2 and the variable x ------> 2x

But, since the sqrts are both irrational then they can be combined into a single sqrt (9) which is equivalent to the rational number 3.

Therefore the final form of the fraction is 2sqrt(3) / 3

Answer 2

2 times the sqrt of 3 is = 2 square root of three.

Answer 3

Ok your right when you multiply the square root of three by the square root of three you get three. But when you multiply 2 times the square root of three the answer is 2rt3.

Answer 4

plz try to understand the process as shown below

When you have:
sqrt(3) * sqrt(3) = 3
If you multiply a radical by itself (and its a square root) the answer is the radicand.
this also means:
sqrt(3) * sqrt(3) = (sqrt(3))^2 =3

Now when you multiply a radical for an integer (let's say 2). you have this:

2 * sqrt(3) = sqrt(3) + sqrt(3)

Answer 5

Ok, lets go step by step.

When you have:
sqrt(3) * sqrt(3) = 3
If you multiply a radical by itself (and its a square root) the answer is the radicand.
this also means:
sqrt(3) * sqrt(3) = (sqrt(3))^2 =3

Now when you multiply a radical for an integer (let's say 2). you have this:

2 * sqrt(3) = sqrt(3) + sqrt(3)


In your problem:

2/sqrt(3)

rationalize means taking all radicals from the denominator. We will multiply the whole expression for sqrt(3)/sqrt(3) - which is another way of saying we will multiply the whole expression for 1.

2/sqrt(3) * sqrt(3)/sqrt(3) =

(2 * srt(3))/(sqrt(3) *sqrt(3))=

(2 * sqrt(3))/3

And thats it.

Answer 6

2/√3

Multiply both numerator and denominator by √3. When you perform this operation you are, in effect, multiplying the expression by one and therefore not changing its value.

2√3/(√3√3)

which reduces to

2√3/3
.

Answer 7

2/rt3

this becomes...

2/rt3 x rt3/rt3

= 2rt3/rt9

= 2rt3/3

You just have to leave it as this.