Question

Find The Least Number With Which 196 Should Be Multiplied To Make It A Perfect Cube

Answer 1

Answer:

Step-by-step explanations

x2=196

X=√196=14

Now,14 is least no. Which multiplied with 196 to make it perfect cube

Answer 2

Answer:

The least number with which 196 should be multiplied to make it a perfect cube is 14.

Step-by-step explanation:

The prime factors of 196 are:

196 = 2 x 2 x 7 X 7

We observe that, if one more 2 & 7 are multiplied by the number then it becomes a perfect cube.

∛196 = ∛2 x 2 x 2 x 7 x 7 x7

        = 2 x 7 = 14

Thus, 2 x 7 = 14 should be multiplied by 196 to make it a perfect cube.

In order of finding the cube root by prime factorization we use the following steps:

• Step I: Obtain the given number.
• Step II: Resolve it into prime factors.
• Step III: Group the factors in 3 in such a way that each number of the group is the same.

For example, The prime factorisation of 216 is as follows:

216 = 2 × 2 × 2 × 3 × 3 × 3

Another example

Question

Find the smallest number by which 243 must be multiplied to obtain a perfect cube?

Solution:

A number is a perfect cube only when each factor in the prime factorization of the given number exists in triplets. Using this concept, the smallest number can be identified.

243 = 3 × 3 × 3 × 3 × 3

= 3³ × 3²

Here, one group of 3's is not existing as a triplet. To make it a triplet, we need to multiply by 3.

Thus, 243 × 3 = 3 × 3 × 3 × 3 × 3 × 3 = 729 is a perfect cube

Hence, the smallest natural number by which 243 should be multiplied to make a perfect cube is 3.