Question

How do you simplify $ \sqrt{100} $ ?

Answer 1

Hint: To simplify $ \sqrt{100} $, we are going to, first of all, find the number whose square is 100. The reason behind that square root means the power of 100 is $ \dfrac{1}{2} $ and when we know the number whose square is 100 then we can write 100 as that number to the power 2 and in the power 2 will be canceled from the numerator and the denominator in the power.

IComplete step by step answer:
n the above problem, the number which we have to simplify is:
 $ \sqrt{100} $
To simplify the above problem, we have to solve this square root. For that, we are going to find the number whose square is 100. If we do the square of the number 10 then we get 100 so we can write 100 as the square of 10. Writing 10 to the power 2 in place of 100 in the above square root we get,
 $ \sqrt{{{\left( 10 \right)}^{2}}} $
We know that square root of any number is the power of $ \dfrac{1}{2} $ of that number so replacing the above square root by $ {{(10)}^{2}} $ to the power $ \dfrac{1}{2} $ we get,
 $ {{\left( {{\left( 10 \right)}^{2}} \right)}^{\dfrac{1}{2}}} $
Also, we know the exponent property that:
 $ {{\left( {{a}^{m}} \right)}^{n}}={{a}^{mn}} $
Using above relation in $ {{\left( {{\left( 10 \right)}^{2}} \right)}^{\dfrac{1}{2}}} $ we get,
 $ {{\left( 10 \right)}^{2\times \dfrac{1}{2}}} $
2 will be cancelled out in the exponent from the numerator and denominator and we are left with:
10
Hence, the simplification of $ \sqrt{100} $ is 10.

Note:
 By solving the above problem one thing you should keep in mind is that if you know the squares of the numbers from 1 to 15 then the amount of time that you take to solve the problem will get shortened.
You can solve the above problem by writing the prime factorization of 100 and then club the factors in such a way so that we can get some number to the power 2. This different method is also correct but it will increase the time to solve the problem.
Prime factorization of 100 is as follows:
 $ 100=2\times 2\times 5\times 5 $
We can also write the above number as:
 $ \begin{align}
  & 100=10\times 10 \\
 & \Rightarrow 100={{\left( 10 \right)}^{2}} \\
\end{align} $
As you can see, two extra steps are required to solve this problem so it’s better if you can remember the square of 10.