Question

the smallest of root 8 + root 5 root 7 + root 6 root 3 + root 3 and root 11 + root 12 is

Answer 1

Given:

Given numbers are: $\sqrt{8}+\sqrt{5}\sqrt{7}+\sqrt{6}\sqrt{3}+\sqrt{3}$ and $\sqrt{11}+\sqrt{12}$

To find:

We need to find the smallest number from the given numbers.

Solution:

Before finding the smallest numbers from the given numbers, we need to find the values of individual roots.

So,

• The value of $\sqrt{8}$ is equal to $2.828$.
• The value of $\sqrt{5}$ is equal to $2.236$.
• The value of $\sqrt{7}$ is equal to $2.645$.
• The value of $\sqrt{6}$ is equal to $2.449$.
• The value of $\sqrt{3}$ is equal to $1.732$.
• The value of $\sqrt{11}$ is equal to $3.316$.
• The value of $\sqrt{12}$ is equal to $3.464$.

Now substitute the above values in given numbers.

$\sqrt{8}+\sqrt{5}\sqrt{7}+\sqrt{6}\sqrt{3}+\sqrt{3}=2.828+(2.236\times2.645)+(2.449\times1.732)+1.732$

                                          $=14.715$

$\sqrt{11}+\sqrt{12}= 3.316+ 3.464$

                 $=6.78$

From the above simplification, it is clear that, second number is smallest when compared to first number.

Therefore, $\sqrt{11}+\sqrt{12}$ is the smallest number.