The square root of a square root?

Question

i have the square root of the square root of 32

at first i thought that the 2 square roots would cancel giving me 32 as an answer but according to the back of the book its wrong?? Help please.

Answer 1

(32^½)^(½)
= 32^(¼)
= (2 x 16)^(¼)
= 2 ( 2 )^(¼)

Answer 2

The SQUARE of a square root would effectively "cancel" the square root. But the square root of a square root would be the quadratic root.

It might help if you think of the square root in exponential form, and use the properties you know for exponents.

√( √32 ) =
√( 32^(1/2) ) =
( 32^(1/2) )^(1/2) =
32^(1/4)

You could then simplify this by going:
(32)^(1/4) =
(16*2)^(1/4) =
(16^(1/4)) (2^(1/4))=
(2^4)^(1/4) (2^(1/4))=
2(2^(1/4))

Answer 3

nope it isnt..
a square root of a square root would look more like x^1/4

so the √√32 =:
=√√(16)(2)
=√4√2
=2√√2
=2(2^1/4) = ans

hope this helps!

Answer 4

you could consider the square root as a power of 1/2, so that the question is now [32^(1/2)]^(1/2). Simplifying with power rules, you attain 32^(1/4) or the quartic root of 32. (multiplying both powers)

Answer 5

the square root of a square root is the fourth root.
what to the fourth power is equal to 32?
split it up. the fourth root of 16 times the fourth root of 2
we know 2^4=16, so the fourth root of 16 =2.
your answer is 2 times the fourth root of 2

Answer 6

the answer is 2 fourth root of 2

Answer 7

The sqrt( sqrt(32)) = sqrt ( sqrt ( 2^5)) = sqrt ( 2^(5/2)) = (2^(5/2) )^(1/2) = 2^(5/4) = 2^(1/4) * 2^(4/4) = 2^(1/4) * 2 = 2 * 4th root of 2.

You can also think of it this way:

sqrt ( sqrt (32)) = sqrt( sqrt(4*4*2)) = sqrt( 4 * sqrt(2)) = 2 * sqrt( sqrt(2)) = 2 * 4th root of 2.

Answer 8

sq.r. of sq.r. of 32= 2^(5/4)=2*[2^(0.25)]

Answer 9

i think it should b 32......if it is not....i dont know why