MATH PEOPLE, HELP ME PLZ! In radical form, what is the square root of the square root of 50?

Question

Also, please explain the process to reach this conclusion. Nobody has helped me so far, and I need to know this in order to use it to solve my question. My problem was....two x squared = five time the square root of 2.

Answer 1

It's not quite clear what you are asking:

IF your problem was 2 x^2 = 5 sqrt(2) or 5 2^1/2, then, simply dividing both sides by 2, :

x^2 = 5 2^(-1/2), so x = 5^(1/2) 2^(-1/4) or "the square root of 5 divided by the fourth root of 2."

(For what it's worth, the NUMERICAL VALUE of this is ~ 1.8803... .)

On the other hand, the square root of the square root of 50 is:

[50^(1/2)]^(1/2),

which is 50^(1/4) since successively applied exponents applied like this MULTIPLY one another. Another way of writing this is 2^(1/4) * 5^(1/2), or "the fourth root of 2 times the square root of 5."

The numerical value for this is: 2.6951... .

So, what is the relation between 50^(1/4) [the "square root of the square root of 50"] and the x in your "additional detail" verbal equation?:

[50^(1/4)] / x = [{2 * 25}^1/4] 2^(1/4) / 5^(1/2) = 2^(1/2) ! (Since 25^(1/4) = 5^(1/2), and 2^(1/4) * 2^(1/4) = 2^(1/2).)

ACID TEST: Let's check the ratio of the two values found earlier:

(2.6951...) / (1.8803...) = 1.4142... YIPPEE! --- I hope that you do indeed recognize this as the square root of 2, to this approximation.

More accurately, with my early 1980s calculator,

2.659147948... / 1.880301547... = 1.414213562...,

while, directly punching in sqrt(2), I get:

sqrt(2) = 1.414213562... They agree; isn't math wonderful ?!

I hope this has helped.

Live long and prosper.

Answer 2

Square root is the same as saying x^1/2, right? Well the square root of x^1/2 is (x^1/2)^1/2. A power to a power means to multiply the exponents, so 1/2 * 1/2 = 1/4. So the square root of a square root is the 4th root.

Answer 3

50^1/4

sqrt = 1/2, therefore 1/2 x 1/2 = 4th root

Answer 4

5square root 2

Answer 5

sq.rt. of 50=5rt2
sq.rt.of sq.rt.of 50
=sq.rt. of 5 rt2
=rt5*rt of rt2

aliter
sq.rt.of 50=(50)^1/2
sq.rt.of sq.rt of 50
[(50)^1/2]^1/2
(50)^1/4

Answer 6

ok
sqrt(50) = sqrt(2*25)
we can look at it like this
sqrt(50) = sqrt(2) * sqrt(25)
sqrt(25) is a perfect square
so we have
5 * sqrt(2)

Answer 7

HAHA!! The answer is 5 sqroot 2 .. I take it you are going to school online... as well as I am .. if you have any more problems hitme up on yahoo messenger ............

Answer 8

SQRT(50) = SQRT(2) x SQRT(5^2).

Answer 9

http://home.earthlink.net/~sondybeamer/homework/algebra/roots/Square_Root.html

2.659147948472