Question

23. Find the cube - roots of 729​

Answer 1

Answer:

Step 1: Find the prime factors of 729

729 = 3 × 3 × 3 × 3 × 3 × 3

Step 2: Clearly, 729 is a perfect cube. Here we will be using laws of exponents.

729 = 36 [am × an = am+n]

729 = [32]3 [(am)n = amn]

729 = 93

Step 3: Now, we will apply cube root to both the sides of the above expression to take out the factor as a single term, which is in cubes.

3√729 = 3√(93)

So, here the cube root is cancelled by the cube of 9.

Hence, 3√729 = 9

Finding the cube root of perfect cubes up to three-digit numbers is easy if we memorise the below-given table.

Number (n)

Cubes (n3)

1

1

2

8

3

27

4

64

5

125

6

216

7

343

8

512

9

729

10

1000

Answer 2

Answer:

9³..................