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 $275=5\times 5\times 11$
 $$\begin{gathered} \Rightarrow \sqrt{275}=\sqrt{5\times 55} \\ \Rightarrow \sqrt{275}=\sqrt{5\times 5\times 11} \end{gathered}$$
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.
 $$\begin{gathered} \Rightarrow \sqrt{275}=5\times 3.3166 \\ \Rightarrow \sqrt{275}=16.5831 \end{gathered}$$

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

Note: Here, the symbol ${}^{\prime }{\sqrt{}}^{\prime }$ 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.