Answer
384.6k+ views
Hint: Square root of a number is a value, which on 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 \[{x^2} = y\]. Here we can see that 294 is not a perfect square. To solve this we factorize the given number.
Complete step-by-step solution:
Given,
\[\sqrt {567} \]
567 can be factorized as,
\[567 = 1 \times 3 \times 3 \times 3 \times 3 \times 7\]
We can see that 3 is multiplied twice two times, we multiply that we get,
\[567 = {3^2} \times {3^2} \times 7\].
Then,
\[ \Rightarrow \sqrt {567} = \sqrt {{3^2} \times {3^2} \times 7} \]
Now we know that square and square root will get cancel and we take term out the radical symbol,
\[ = 3 \times 3\sqrt 7 \]
\[ = 9\sqrt 7 \]. This is the exact form. We can stop here.
We also put it in the decimal form.
We know that \[\sqrt 7 = 2.645\] and multiplying this with 9 we get,
\[ = 9 \times 2.645\]
\[ = 23.81\]. This is the decimal form.
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. To find the factors, find the smallest prime number that divides the given number and divide it by that number, and then again find the smallest prime number that divides the number obtained and so on. The set of prime numbers obtained that are multiplied to each other to form the bigger number are called the factors.
Complete step-by-step solution:
Given,
\[\sqrt {567} \]
567 can be factorized as,
\[567 = 1 \times 3 \times 3 \times 3 \times 3 \times 7\]
We can see that 3 is multiplied twice two times, we multiply that we get,
\[567 = {3^2} \times {3^2} \times 7\].
Then,
\[ \Rightarrow \sqrt {567} = \sqrt {{3^2} \times {3^2} \times 7} \]
Now we know that square and square root will get cancel and we take term out the radical symbol,
\[ = 3 \times 3\sqrt 7 \]
\[ = 9\sqrt 7 \]. This is the exact form. We can stop here.
We also put it in the decimal form.
We know that \[\sqrt 7 = 2.645\] and multiplying this with 9 we get,
\[ = 9 \times 2.645\]
\[ = 23.81\]. This is the decimal form.
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. To find the factors, find the smallest prime number that divides the given number and divide it by that number, and then again find the smallest prime number that divides the number obtained and so on. The set of prime numbers obtained that are multiplied to each other to form the bigger number are called the factors.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)