Question

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

Answer 1

Answer:

The correct answer is second option 5 1/2

Step-by-step 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

Answer:

The value is 5 1/2 ⇒ second answer

Step-by-step 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 = $(7^{3})^{\frac{1}{3}}$

* WE will use the rule ⇒ $(b^{m})^{n}=b^{mn}$

∴ $(7^{3})^{\frac{1}{3}}=7^{3*\frac{1}{3}}=7^{1}=7$

* We will do the same with ∛(-8)

∵ -8 = -2 × -2 × -2 = (-2)³

∴∛(-8) = $((-2)^{3})^{\frac{1}{3}}=(-2)^{3*\frac{1}{3}}=(-2)^{1}=(-2)$

* 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