Question

$225$ can be expressed as,

A) $5 \times {3^2}$ 

B) ${5^2} \times 3$ 

C) ${5^2} \times {3^2}$ 

D) ${5^3} \times 3$ 

Answer 1

Hint: Here we solve the problem by using the concept of  Prime factorization.

The process of factoring a number into its prime numbers, or factors, is known as prime factorization. In other words, it is splitting up numbers into its prime factors.

For example: For the number $20$, 

we can write as $20= 2 \times 10$, In this step only $2$ is a prime number, again we will split $10$.

 $20 = 2 \times 2 \times 5$, here the numbers $2,2,5 $ are all prime numbers. So, the prime factors of $20$ will be $2^2 \times 5$.

Using the same procedure we will find the prime factors of $225$.

Complete step-by-step solution:

The given number is $225$ 

The prime factors of $225$ are $3 \times 3 \times 5 \times 5$. 

The prime factors of $225$  contains

$2$  number of $5's$ , and 

$2$  number of $3's$

Therefore, the number $225$ can be expressed as ${5^2} \times {3^2}$ .

Hence, the correct option is (C).

Note: The important step is to write the factors of a number. Once the factors are written, they can be raised to the power in which they occur in the number.

We can represent the prime factorization of a number in the factor tree.

Factor tree of $125$ is shown below: 

In step 1, $125$ is split into $5$ and $25$. $25$ is not a prime number, so we split it into $5$ and $5$.