Question

the product of cube root of 4 and 4 root of 8

Answer 1

Answer:

the value of  $\sqrt[3]{4}$ X $\sqrt[4]{8}$  is       $2. \sqrt[12]{32}$

Step-by-step explanation:

we have to find the product of ( cube root of 4 and 4th root of 8)

= $\sqrt[3]{4}$ X $\sqrt[4]{8}$

it can be written in same form as :

$\sqrt[3]{4}$ X $\sqrt[4]{(4)(2)}$

= $\sqrt[3]{4}$ X $\sqrt[4]{4} \sqrt[4]{2}$

the above form can be represented as :

$[4^{(1/3)}] [4^{(1/4)}] [2^{(1/4)}]$

from first two terms of above , since bases are equal; we can add powers.

$[4^{(1/3)+(1/4)}] [2^{1/4} ]$

= $[4^{(7/12)}] [2^{1/4}]$

we know that '4' can be written as 2²

= $[2^{(7/12)(2)}] [2^{1/4}]$

= $[2^{7/6}] [2^{1/4}]$

add powers of above form:

= $2^{(7/6) + (1/4)}$

= $2^{17/12}$

it can also be written as :

= $2^{(5/12)+1}$

= [tex]2^{1} . 2^{(5/12)}\\ 2. \sqrt[12]{2^{5} } [/tex]

= $2. \sqrt[12]{32}$

the value of  $\sqrt[3]{4}$ X $\sqrt[4]{8}$  is       $2. \sqrt[12]{32}$





Answer 2

Answer:

Product of cube root of 4 and 4 root of 8 is 17.952

Step-by-step explanation:

In context to the given question we have to find the product of the following

i.e.

=(³√4) x (4√8)

=(4¹/³) x (4(2√2))

=(4¹/³) x (8√2)

= (4¹/³) x (8) x (2¹/²)

= 1.587 x 8 x 1.414

= 17.952

Therefore; product of cube root of 4 and 4 root of 8 is 17.952