lucas211 wrote:Which of the following is the value of √3√0,000064 ?

A) 0,004
B) 0,008
C) 0,02
D) 0,04
E) 0,2

thanks in advance

The problem statement is very misleading. Make sure you type the problem correctly

(3√0,000064)^(1/2) Or [(0.000064)^(1/3) ]^(1/2)

Start from the inner most value.

0.000064 = 64/1000000
(0.000064)^(1/3) = 4/100
{(0.000064)^(1/3) ]^(1/2) = (4/100)^(1/2) = 2/10

Correct Option: E

The problem statement is very misleading. Make sure you type the problem correctly

Hi OptimusPrep

Thanks for the notice. I have updated the original post.

Nice question. I am having hard time solving it. But thanks to the one who has solution to it

√(∛0.000064)

= √[ (64 * 10¯â�¶)¹"²Â³ ]

= √(4 * 10¯²)

= (4 * 10¯²)¹"²Â²

= 2 * 10¯¹

= 0.2.

The correct answer is E.

√∛0.000064 =>

√∛64/1000000 =>

√∛(2�/10�) =>

√(2²/10²) =>

2/10

lucas211 wrote:Hello BTG

would appreciate a little help on the following question:

Let's review the notation first. When an exponent is a fraction, that exponent indicates taking a root. So, if we have for example 27^1/3, the 1/3 instructs us to take the cube root of 27, which is 3. Similarly, if the exponent were 1/2, as in 25^1/2, the 1/2 instructs us to take the square root of 25, which is 5.

To solve this question, we can refer to two rules:

1) If a decimal with a finite number of decimal places is a perfect cube, its cube root will have exactly one-third of the number of decimal places. Thus, a perfect cube decimal must have a number of decimal places that is a multiple of 3.

2) If a decimal with a finite number of decimal places is a perfect square, its square root will have exactly half of the number of decimal places. Thus, a perfect square decimal must have an even number of decimal places.

Let's look first at (0.000064)^1/3. The 1/3 instructs us to take the cube root of 0.000064. By rule number 1, the cube root of 0.000064 = 0.04. We were able obtain this value because 0.000064 has 6 DECIMAL PLACES and because the cube root of 64 is 4.

The problem now looks like this: (0.04)^1/2. The ½ instructs us to find the square root of 0.04. By rule number 2, the square root of 0.04 = 0.2. We were able to obtain this value because 0.04 has 2 DECIMAL PLACES and the square root of 4 is 2.

Answer: E