Question

How do you simplify the square root of $ 275? $

Answer 1

Hint: A positive integer, when multiplied by itself gives the square of a number. The square root of the square of an integer gives the original number. To find the square root of $ 275 $ , we simply need to factorize the given number inside the square root and then take out the repeating number and write it once outside the square root.

Complete step-by-step solution:
To simplify the square root of $ 275 $ , first of all factorize $ 275 $ .
Factors of $ 275 = 5 \times 5 \times 11 $
 $
   \Rightarrow \sqrt {275} = \sqrt {5 \times 55} \\
   \Rightarrow \sqrt {275} = \sqrt {5 \times 5 \times 11} \\
  $
Here, $ 5 $ is repeated two times, so we write it as $ {5^2} $ inside the square root.
 $ \Rightarrow \sqrt {275} = \sqrt {{{\left( 5 \right)}^2} \times 11} $
Now, we know that we can cancel square and square root and we can take the term out of square root.
 $ \Rightarrow \sqrt {275} = 5\sqrt {11} $
This is the final form and our final answer.
We can also write it in decimal form by writing the value of $ \sqrt {11} $ .
We know that the value of $ \sqrt {11} $ is $ 3.3166 $ . So, by multiplying it with $ 5 $ , we get our answer in decimal form.
 $
   \Rightarrow \sqrt {275} = 5 \times 3.3166 \\
   \Rightarrow \sqrt {275} = 16.5831 \\
  $

Hence, the simplified form of $ \sqrt {275} $ is $ 5\sqrt {11} $ and the decimal form is $ 16.5831 $ .

Note: Here, the symbol $ '\sqrt {} ' $ is called Radical and the number inside the symbol is called a radicand. Square root of any number is calculated by prime factoring the given number inside the square root itself. Prime factorization means expressing the number in the form of a product of the prime numbers used to construct the number.