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Express as a mixed number:

\(\sqrt{0.64}-\sqrt[3]{-0.008}+\sqrt[4]{\frac{4}{20.25}}+\sqrt[5]{16\div\frac{1}{2}}\)

Guest Feb 23, 2019

#1**+1 **

First, let's find out what each of those expressions boils down to.

square root 0**.**64 -- well, this is plus or minus 0**.**8 but I'm going to use only the positive value = 0**.**8 = 8/10

cube root –0**.**008 -- this equals –0**.**2 = –2/10

fourth root 4/20**.**25 -- I had to use the calculator to determine this is 0**.**666666••• = 2/3

fifth root (16 ÷ 1/2) -- same as fifth root of 32 which is 2

put them together 8/10 – (–2/10) + 2/3 + 2/1

a common denominator of 30 will work, so 24/30 + 6/30 + 20/30 + 60/30 = 110/30 = 3 20/30 = 3 2/3

Guest Feb 23, 2019

edited by
Guest
Feb 23, 2019

edited by Guest Feb 23, 2019

edited by Guest Feb 23, 2019

#2**+1 **

It's too late for me to edit my answer above. I woke up this morning with a better reduction of the fourth root element of the equation.

the fourth root of (4/20**.**25)

a fourth root of a number is simply the square root __of__ the square root of the number

we recognize that both the numerator and denominator are squares, so let's take those square roots

the square root of 4 is 2 and the square root of 20**.**25 is 4**.**5 (more about this below)

so the fourth root of (4/20**.**25) is the same as the square root of (2/4**.**5)

let's multiply (2/4**.**5) by (2/2) under the radical, and we have the square root of 4/9 which = 2/3

20**.**25 is recognizable as the square of 4**.**5, because 20 = 4x5

We can square any number that ends in 5 by addressing the 5 separately from the number ahead of it

Consider 4**.**5 as a 4 and a **.**5. Square the **.**5 to get **.**25 and set it aside mentally.

Take the 4 and add 1 to it and multiply the two numbers - i.e., 4x5 - to get 20.

Put the 20 and the **.**25 together, and get 20**.**25

Do this again with another example, any number that ends with 5 .... so let's go with 85

Square the 5 to get 25 and set it aside mentally

Add 1 to the 8 and multiply 8 by that 9 - i.e., 8x9 - to get 72

Combine the 72 and the 25 giving us the answer ... 85 squared is 7225

Guest Feb 23, 2019

edited by
Guest
Feb 23, 2019

#3**0 **

Here is my take :)

\(\sqrt{0.64}-\sqrt[3]{-0.008}+\sqrt[4]{\frac{4}{20.25}}+\sqrt[5]{16\div\frac{1}{2}}\\ =0.8-\sqrt[3]{-1*8*0.001}+\sqrt[4]{\frac{4}{2025\div100}}+\sqrt[5]{32}\\ =0.8-(-0.2)+\sqrt[4]{\frac{4*100}{2025}}+2\\ =0.8+0.2+\sqrt[2]{\frac{2*10}{45}}+2\\ =3+\sqrt[2]{\frac{2*10}{5*9}}\\ =3+\sqrt[2]{\frac{2*2}{9}}\\ =3+\frac{2}{3}\\ =3\frac{2}{3}\\\)

.Melody Feb 23, 2019