how can u simplify radicals like this?

Question

128/ 2... pretend that both of the numbers have radical sign ..because i can't do it here.... how can i simplify this...

another example.... 5*10... pretend that every number has radical sign... please help me

Answer 1

√128 / √2

Rationalizing the denominator

√128 √2 / √2√2 =

√256 / √4

Square root the numerator and denominator

16 / 2 =

8

- - - - - - -s-

Answer 2

A radical sign indicates you are finding the square root so use sqrt(128)/sqrt(2) for your problem.

Two basic rules of radicals or roots:

1) The sqrt of a product is the product of the square roots

2) The sqrt of a quotient is the quotient of the square roots.

Learn to understand and use these properties and the problems become easy.

So, sqrt(128) / sqrt(2) = sqrt[128/2] = sqrt(64) = 8.

The second problem is sqrt(5)*sqrt(10) and is equal to

sqrt(5*10) = sqrt(50) = sqrt(25*2) = sqrt(25)*sqrt(2) = 5sqrt(2)

Become familiar with perfect squares such as 4,9,16,25,36,49, etc and factor numbers such as 50 into
25*2 so you can take the square root of the perfect square 25.

Answer 3

√128/√2

=√(64*2) / √2
= 8√2 / √2

The √2 cancels, leaving us with ♥8♥.



√5 * √ 10
= √5 * √ (5*2
= √5 * √5 * √2
= √5² * √2
♥= 5√2♥

Answer 4

sqrt(m)/sqrt(n) = sqrt(m/n)
So sqrt(128)/sqrt(2) = sqrt(128/2) = sqrt(64) = 8

sqrt(5)/sqrt(10) = sqrt(5/10) = sqrt(1/2)
= sqrt(1)/sqrt(2) = 1/sqrt(2) = sqrt(2)/(sqrt(2)(sqrt(2)=sqrt(2)/2

We could have stopped at 1/sqrt(2) but most mathemeticians do not like to leave a square root in the denominator of a fraction. To get rid of it simply multiply both numerator and denominator by the sqrt of the denominator.

Thus 1/sqrt(3) = 1*sqrt(3)/[sqrt(3)*sqrt(3)] = sqrt(3)/3

Answer 5

I'm gonna write out what I think you're trying to indicate and work from there.

The first one: (sqrt)128/(sqrt)2
The second one: (sqrt)5*(sqrt)10

There are two properties that hold true for radicals. They are
(sqrt)a/(sqrt)b = (sqrt)(a/b) and
(sqrt)a * (sqrt)b = (sqrt)(a*b)

1. (sqrt)128/(sqrt)2 = (sqrt)(128/2) =
(sqrt)(64) =
8

2. (sqrt)5*(sqrt)10 = (sqrt)(5*10) =
(sqrt)50
Now this one can be broken down further. You find out if it has a factor that is a perfect square. In this case, 25 is a factor of 50.
(sqrt)(25*2) =
(sqrt)25 * (sqrt)2
5(sqrt)2