Question

Solve the following based on the instructions given:

(1) Cube root of 729 (Write in symbols)
(2) 25 + x (Write the degree of the polynomials)
(3) $\sqrt[3]{-512}=-8$ (Write in words)
(4) (13)³ (Evaluate)
(5) $m-\frac{1}{m}+4$ (Write giving reasons whether it is a polynomial or not)
(6) −343 (Write the number whose cube is the given number)

Answer 1

(1) The cube root of 729 is 9. It can be written as: $\sqrt[3]{729}=9$

(2) 25 + x
The highest index of a variable in the polynomial is 1; so, the degree of the polynomial is 1.

(3) The cube root of −512 is −8.

(4) (13)³
It can be expressed and solved as:
13³ = 13 × 13 × 13 = 169 × 13 = 2197
∴ 13³ will be equal to 2197.

(5) $m-\frac{1}{m}+4=m-m^{-1}+4$
The given expression has a negative index of variable. So, it is not a polynomial expression

(6) Cube root of −343 can be calculated by finding the cube root of 343.
343 = 7 × 49
= 7 × 7 × 7
∴ 343 = (7 × 7 × 7)
∴ $\sqrt[3]{343}$ = 7
∴ $\sqrt[3]{-343}$ = −7