Answer
Verified
384.3k+ views
Hint:
Here, we have to find the square root of a given number. We can find the square root of the number by using the Prime Factorization methods. The square root of any number is equal to a number, which when squared gives the original number.
Formula Used: The square root of a number is given by the formula: \[y = \sqrt a \]where \[a\] is the given number.
Complete step by step solution:
We have to find the square root of 256.
Now, we are using the prime factorization method to find the square root.
Now, we have to find the prime factors.
As 256 is an even number, we will start dividing it by least prime number 2. Therefore, we get
\[256 \div 2 = 128\]
Now 128 is again an even number, so dividing it by 2, we get
\[128 \div 2 = 64\]
64 is again an even number, so dividing it by 2, we get
\[64 \div 2 = 32\]
Now dividing 32 by 2, we get
\[32 \div 2 = 16\]
Dividing 16 by 2, we get
\[16 \div 2 = 8\]
Dividing 16 by 2, we get
\[8 \div 2 = 4\]
Dividing 16 by 2, we get
\[4 \div 2 = 2\]
Now as we have got the quotient as a prime number, we will not divide the number further.
Thus, we can write 256 as
\[256 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2\]
Now, we have to find the square root by using the prime factors.
Taking square root on both sides of the above equation, we get
\[ \Rightarrow \sqrt {256} = \sqrt {2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2} \]
Now, we will get
\[ \Rightarrow \sqrt {256} = 2 \times 2 \times 2 \times 2\]
Multiplying the terms, we have
\[ \Rightarrow \sqrt {256} = 16\]
Therefore, the square root of the number 256 is 16.
Note:
The square root of the number can also be found using the method of long division method. The Long Division method is a method which can be used for imperfect numbers too.
Therefore, the square root of 256 is 16.
If a number ends with 2, 3, 7 or 8 (in the unit digit), then the perfect square root does not exist. If a number ends with 1, 4, 5, 6 or 9 in the unit digit, then the number will have a square root. Prime factorization is a process of factoring a number in terms of prime numbers i.e. the factors will be prime numbers.
Here, we have to find the square root of a given number. We can find the square root of the number by using the Prime Factorization methods. The square root of any number is equal to a number, which when squared gives the original number.
Formula Used: The square root of a number is given by the formula: \[y = \sqrt a \]where \[a\] is the given number.
Complete step by step solution:
We have to find the square root of 256.
Now, we are using the prime factorization method to find the square root.
Now, we have to find the prime factors.
As 256 is an even number, we will start dividing it by least prime number 2. Therefore, we get
\[256 \div 2 = 128\]
Now 128 is again an even number, so dividing it by 2, we get
\[128 \div 2 = 64\]
64 is again an even number, so dividing it by 2, we get
\[64 \div 2 = 32\]
Now dividing 32 by 2, we get
\[32 \div 2 = 16\]
Dividing 16 by 2, we get
\[16 \div 2 = 8\]
Dividing 16 by 2, we get
\[8 \div 2 = 4\]
Dividing 16 by 2, we get
\[4 \div 2 = 2\]
Now as we have got the quotient as a prime number, we will not divide the number further.
Thus, we can write 256 as
\[256 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2\]
Now, we have to find the square root by using the prime factors.
Taking square root on both sides of the above equation, we get
\[ \Rightarrow \sqrt {256} = \sqrt {2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2} \]
Now, we will get
\[ \Rightarrow \sqrt {256} = 2 \times 2 \times 2 \times 2\]
Multiplying the terms, we have
\[ \Rightarrow \sqrt {256} = 16\]
Therefore, the square root of the number 256 is 16.
Note:
The square root of the number can also be found using the method of long division method. The Long Division method is a method which can be used for imperfect numbers too.
Therefore, the square root of 256 is 16.
If a number ends with 2, 3, 7 or 8 (in the unit digit), then the perfect square root does not exist. If a number ends with 1, 4, 5, 6 or 9 in the unit digit, then the number will have a square root. Prime factorization is a process of factoring a number in terms of prime numbers i.e. the factors will be prime numbers.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Why Are Noble Gases NonReactive class 11 chemistry CBSE
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
At which age domestication of animals started A Neolithic class 11 social science CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
Write a letter to the principal requesting him to grant class 10 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE