Question

How do you simplify the square root\[\sqrt {45} \] of ?

Answer 1

Hint:
We have given a number and we have to simplify its square root. For this we have to simplify its square root. For this we have to find the prime factor of the number by prime factorization method. Then we write the number equal to the product of the prime factor. Take a square on both sides .Now the prime number which are in pair under root will come out as a single number; other prime numbers which are not in pair will remain in the square root. This will give the square root. This will give the square root of the given number.

Complete Step by step Solution:
The given number is \[45\].We have to simplify its square root. Firstly, we write its prime factors. The prime factors of \[45\] are \[3,{\text{ }}3,\] and \[5\].
Therefore \[45 = 3 \times 3 \times 5\]
Taking square root on both sides
\[\sqrt {45} = \sqrt {3 \times 3 \times 5} \]
Since \[3\] is in pair so we take \[3\] out of square root. \[5\] is not in pair so it will remain in square root.
\[\sqrt {45} = 3 \times \sqrt 5 \]
\[ \Rightarrow \sqrt {45} = 3\sqrt 5 \]

the square root of \[45 = 3\sqrt 5 \].

Note:
Prime numbers are those numbers which are divided by one and itself only .In the number theory integer factorization is the decomposition of the composite number into the smaller integer. If their smaller integers are restricted to prime number only the process is called prime factorization. Square root of a number is the number which when multiplied by itself gives the number. Example when we multiply \[4\] by \[4\] we get \[16\] so \[4\] is the square root of \[16\].