Question

Please help me, aswell as explain how to do it!

Answer 1

The correct answer is second option 5 1/2

Explanation:

It is given that,

∛343 + 3/4 ∛-8

To find the value of ∛343 + 3/4 ∛-8

We have ∛343 = 7 and ∛-8 = -2

∛343 + 3/4 ∛-8 = 7 +( 3/4 * -2)

= 7 + (-3/2)

= 7 - 3/2

= (14 - 3)/2

= 11/2 = 5 1/2

Therefore the correct answer is second option

Answer 2

The value is 5 1/2 ⇒ second answer

Explanation:

* At first we must simplify each radical and then add the terms

- To simplify the cube root lets change the number under it

to a number with power of 3 and then change radical to

a rational exponent

∵ ∛x = x^1/3

∵ 343 = 7 × 7 × 7 = 7³

∴∛343 =
`(7^(3))^{(1)/(3)}`

* WE will use the rule ⇒
`(b^(m))^(n)=b^(mn)`

∴
`(7^(3))^{(1)/(3)}=7^{3*(1)/(3)}=7^(1)=7`

* We will do the same with ∛(-8)

∵ -8 = -2 × -2 × -2 = (-2)³

∴∛(-8) =
`((-2)^(3))^{(1)/(3)}=(-2)^{3*(1)/(3)}=(-2)^(1)=(-2)`

* Lets solve the problem

# ∛343 + 3/4 (∛-8) = 7 + (3/4) × (-2) =

7 + (-3/2) = 11/2 = 5 1/2

* The value is 5 1/2