Answer
Verified
379.8k+ views
Hint: In the given question, we are required to show that number provided to us, $ 500 $ is not a perfect square. So, in order to show that the given number is not a perfect square, we will try to compute the square root of the value. Square root of a number is a value, which when multiplied by itself gives the original number. Suppose, ‘x’ is the square root of ‘y’, then it is represented as $ x = \sqrt y $ or we can express the same equation as $ {x^2} = y $ .
Complete step-by-step answer:
We have to show that the number $ 500 $ is not a perfect square. So, we try to find the square root of the number. If in any case, the square root of the number comes out to be a positive integer, then the number is a perfect square. Otherwise, the number is not a perfect square.
$ 500 $ can be factorized as,
$ 500 = 2 \times 2 \times 5 \times 5 \times 5 $
Now, we can see that $ 2 $ is multiplied twice, so we write in exponential form and raise $ 2 $ to the power $ 2 $ . Similarly, we can see that $ 5 $ is multiplied thrice, so we write in exponential form and raise $ 5 $ to the power $ 3 $ . So, we get,
$ \Rightarrow 500 = {2^2} \times {5^3} $
Now, $ \sqrt {500} = \sqrt {{2^2} \times {5^3}} $
We know that $ {5^3} = {5^2} \times 5 $ . So, $ {5^3} $ can be written as $ {5^2} \times 5 $
Now, $ \sqrt {500} = \sqrt {{2^2} \times {5^2} \times 5} $
Since we know that $ {2^2} $ and $ {5^2} $ are perfect squares. So, we can take these outside of the square root. So, we have,
So, \[\sqrt {500} = 2 \times 5 \times \sqrt 5 \]
Since $ 5 $ is not a square number, we keep it inside the square root.
$ \Rightarrow \sqrt {500} = 10\sqrt 5 $
This is the simplified form of $ \sqrt {500} $ .
Now, we see that the square root of the number $ 500 $ is not a perfect square as the prime factors of the number are not in pairs. So, we can conclude that the number $ 500 $ is not a perfect square.
Note: Here $ \sqrt {} $ is the radical symbol used to represent the root of numbers. The number under the radical symbol is called radicand. The positive number, when multiplied by itself, represents the square of the number. The square root of the square of a positive number gives the original number.
Complete step-by-step answer:
We have to show that the number $ 500 $ is not a perfect square. So, we try to find the square root of the number. If in any case, the square root of the number comes out to be a positive integer, then the number is a perfect square. Otherwise, the number is not a perfect square.
$ 500 $ can be factorized as,
$ 500 = 2 \times 2 \times 5 \times 5 \times 5 $
Now, we can see that $ 2 $ is multiplied twice, so we write in exponential form and raise $ 2 $ to the power $ 2 $ . Similarly, we can see that $ 5 $ is multiplied thrice, so we write in exponential form and raise $ 5 $ to the power $ 3 $ . So, we get,
$ \Rightarrow 500 = {2^2} \times {5^3} $
Now, $ \sqrt {500} = \sqrt {{2^2} \times {5^3}} $
We know that $ {5^3} = {5^2} \times 5 $ . So, $ {5^3} $ can be written as $ {5^2} \times 5 $
Now, $ \sqrt {500} = \sqrt {{2^2} \times {5^2} \times 5} $
Since we know that $ {2^2} $ and $ {5^2} $ are perfect squares. So, we can take these outside of the square root. So, we have,
So, \[\sqrt {500} = 2 \times 5 \times \sqrt 5 \]
Since $ 5 $ is not a square number, we keep it inside the square root.
$ \Rightarrow \sqrt {500} = 10\sqrt 5 $
This is the simplified form of $ \sqrt {500} $ .
Now, we see that the square root of the number $ 500 $ is not a perfect square as the prime factors of the number are not in pairs. So, we can conclude that the number $ 500 $ is not a perfect square.
Note: Here $ \sqrt {} $ is the radical symbol used to represent the root of numbers. The number under the radical symbol is called radicand. The positive number, when multiplied by itself, represents the square of the number. The square root of the square of a positive number gives the original number.
Recently Updated Pages
what is the correct chronological order of the following class 10 social science CBSE
Which of the following was not the actual cause for class 10 social science CBSE
Which of the following statements is not correct A class 10 social science CBSE
Which of the following leaders was not present in the class 10 social science CBSE
Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE
Which one of the following places is not covered by class 10 social science CBSE
Trending doubts
Harsha Charita was written by A Kalidasa B Vishakhadatta class 7 social science CBSE
Which are the Top 10 Largest Countries of the World?
Banabhatta wrote Harshavardhanas biography What is class 6 social science CBSE
Difference Between Plant Cell and Animal Cell
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE