Question

Use prime factorisation to find the square root of \[1225\].
A) $122$
B) $225$
C) $35$
D) $50$

Answer 1

Hint: We will find the numbers that divide the given number completely and then we will use the prime factorisation to write the given number as the product of the prime factors. Then we will select the common factors and then we will select only one of each pair. The product of such selected factors will be the square root.

Complete step-by-step answer:
The given number is $1225$.
We have to find the square root of the given number. This means that we have to find the real number such that this product with itself gives us the answer $1225$.
We have to express the given number as a product of prime numbers.
We observe that the given number has $5$ at the units place thus, it is divisible by $5$ .
Thus, we can write the given number as:
$\Rightarrow$$1225 = 5 \times 245$
Again, the number is divisible by $5$, which implies the following:
$\Rightarrow$$1225 = 5 \times 5 \times 49$
Now the number $49$ is divisible by $7$ .
Therefore, we get the following:
$\Rightarrow$$1225 = 5 \times 5 \times 7 \times 7$
Now we have two pairs one with two $5$ and another with two $7$.
Thus, product of these numbers taken once will indicate the square root of the given number as follows:
$\Rightarrow$$\sqrt {1225} = 5 \times 7$
On simplifying we can write the following:
$\Rightarrow$$\sqrt {1225} = 35$

Hence the correct option is C.

Note: We started by expressing the given number as a product of prime numbers. This is called the prime factorisation of the number. Then we divide the prime factors in the pairs. If a number is not paired with any other number we can conclude that the square root is going to be an irrational number. If we have perfect pairs then we take a single number from the pair and take the product of all such numbers to find the square root of the given number.