Question

Simplify \[\sqrt {100} + \sqrt {36} \]

Answer 1

Hint: First find the factors of the given numbers to find the square roots and then add them up. The factors of a number are the divisor which will completely divide the number without leaving any remainder. To find the square root of a number by prime factorization method, first divide the given number to its prime factor then make the pair of similar factor, so that factor in each pair is equal then square root all the pair of factor and find the product of factor. The square root of a number is a number whose square is equal to the original number. The numbers which are divisible by 1 and by itself only, i.e., it should have only two factors is known as Prime numbers.

Complete step-by-step answer:
Given the numbers to simplify is \[\sqrt {100} + \sqrt {36} \]
First we will find the square roots of both the numbers by finding their prime factors
The prime factor of 100
 \[
   2\underline {\left| {100} \right.} \\
   2\underline {\left| {50} \right.} \\
   5\underline {\left| {25} \right.} \\
   5 \\
 \]
Hence the factor of \[\left( {100} \right) = 2 \times 2 \times 5 \times 5\]
Now we will pair all the similar factors in group of two as
 \[
  \left( {100} \right) = \underline {2 \times 2} \times \underline {5 \times 5} \\
   = 2 \times 5 \\
   = 10 \\
 \]
Hence we get the square root of the number 100 as \[ = 10\]
Similarly for the square root of 36
First we will find the prime factor of 36
 \[
   2\underline {\left| {36} \right.} \\
   2\underline {\left| {18} \right.} \\
   3\underline {\left| 9 \right.} \\
   3 \\
 \]
Hence the factor of \[\left( {36} \right) = 2 \times 2 \times 3 \times 3\]
Now we will pair all the similar factors in group of two as
 \[
  \left( {36} \right) = \underline {2 \times 2} \times \underline {3 \times 3} \\
   = 2 \times 3 \\
   = 6 \;
 \]
Hence we get the square root of the number 36 as \[ = 6\]
Now since we have got the value of the square roots of the numbers, so we will add them up together as
 \[
  \sqrt {100} + \sqrt {36} \\
   = 10 + 6 \\
   = 16 \;
 \]
Hence we can say \[\sqrt {100} + \sqrt {36} = 16\]
So, the correct answer is “16”.

Note: Always find the prime factor of the number and group them into the pairs of similar factors. Another way of determining the square root of a number is by long division method, which is more complex, and the chances of getting an error are more.