Answer
Verified
365.7k+ views
Hint:
First, we need to find the factors of the given number to calculate the square root. Factors are the number that completely divides the number without leaving any remainder behind. The square root of a $\sqrt {160} $ can be calculated by prime factorization of the number. Prime factorization is defined as expressing a number as a product of prime numbers. The numbers which are divisible by 1 and itself, i.e., it should only have two factors are called prime numbers.
Complete Step By Step answer:
Given the number to simplify is $\sqrt {160} $
First, we will find the square root of $160$ by finding its prime factors. The square root of a number can be simplified by prime factorization of the number.
Prime factorization involves expressing a number as a product of prime numbers.
The prime factor of $160$
$
2|160 \\
2|80 \\
2|40 \\
2|20 \\
2|10 \\
5 \\
$
Hence the factor of $\left( {160} \right) = 2 \times 2 \times 2 \times 2 \times 2 \times 5$
Now we will pair the similar factors in a group of two,
Therefore,
$
\Rightarrow \sqrt {160} = \sqrt {2 \times 2 \times 2 \times 2 \times 2 \times 5} \\
\Rightarrow \sqrt {160} = \sqrt {{2^2} \times {2^2} \times {2^1} \times 5} \\
$
After forming a pair of the similar factors, we will take a pair out of the square root and thus, continue this process to simplify and attain the answer.
$
\Rightarrow \sqrt {160} = 2 \times 2\sqrt {2 \times 5} \\
\Rightarrow \sqrt {160} = 4\sqrt {10} \\
$
Hence, we get the square root of $160$ is $4\sqrt {10} $
Note:
The square root of any number is calculated by prime factorization of the number. After prime factorization which involves expressing a number as a product of prime numbers (numbers which are divisible by and itself), we need to pair the similar factors in a group of two. Another way to simplify the square root of any number is by using the long division method, which is quite complex, and thus, the chances of getting any error are high.
First, we need to find the factors of the given number to calculate the square root. Factors are the number that completely divides the number without leaving any remainder behind. The square root of a $\sqrt {160} $ can be calculated by prime factorization of the number. Prime factorization is defined as expressing a number as a product of prime numbers. The numbers which are divisible by 1 and itself, i.e., it should only have two factors are called prime numbers.
Complete Step By Step answer:
Given the number to simplify is $\sqrt {160} $
First, we will find the square root of $160$ by finding its prime factors. The square root of a number can be simplified by prime factorization of the number.
Prime factorization involves expressing a number as a product of prime numbers.
The prime factor of $160$
$
2|160 \\
2|80 \\
2|40 \\
2|20 \\
2|10 \\
5 \\
$
Hence the factor of $\left( {160} \right) = 2 \times 2 \times 2 \times 2 \times 2 \times 5$
Now we will pair the similar factors in a group of two,
Therefore,
$
\Rightarrow \sqrt {160} = \sqrt {2 \times 2 \times 2 \times 2 \times 2 \times 5} \\
\Rightarrow \sqrt {160} = \sqrt {{2^2} \times {2^2} \times {2^1} \times 5} \\
$
After forming a pair of the similar factors, we will take a pair out of the square root and thus, continue this process to simplify and attain the answer.
$
\Rightarrow \sqrt {160} = 2 \times 2\sqrt {2 \times 5} \\
\Rightarrow \sqrt {160} = 4\sqrt {10} \\
$
Hence, we get the square root of $160$ is $4\sqrt {10} $
Note:
The square root of any number is calculated by prime factorization of the number. After prime factorization which involves expressing a number as a product of prime numbers (numbers which are divisible by and itself), we need to pair the similar factors in a group of two. Another way to simplify the square root of any number is by using the long division method, which is quite complex, and thus, the chances of getting any error are high.
Recently Updated Pages
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
What organs are located on the left side of your body class 11 biology CBSE
Write an application to the principal requesting five class 10 english CBSE
What is the type of food and mode of feeding of the class 11 biology CBSE
Name 10 Living and Non living things class 9 biology CBSE