Question

Simplify the expression $\sqrt {72} + \sqrt {800} - \sqrt {18} $

Answer 1

Hint: According to given in the question we have to find the value of the expression $\sqrt {72} + \sqrt {800} - \sqrt {18} $ so, to solve the given expression first of all we have to solve the each three terms of the expression as $\sqrt {72} $, $\sqrt {800} $, and $\sqrt {18} $ separately with the help of the finding the square roots of the each terms according to the formula as given below:

Formula used:
$\sqrt {a \times a} = a$ or $\sqrt {{a^2}} = a$……………(1)
So with the help of the formula (1) we can find the square root of the given terms and after finding the square root of all the terms separately we have to put them all in the given expression. Now, we will common the terms that can be and add and subtract the remaining terms of the given expression to simplify it.

Complete step by step answer:
Step 1: Now, first of all we have to solve the first term of the expression which is $\sqrt {72} $ with the help of the formula (1) as mentioned in the solution hint.
$ \Rightarrow \sqrt {72} = \sqrt {9 \times 8} $
Now, we will try to make squares of the terms inside the square root.
\[
   \Rightarrow \sqrt {72} = \sqrt {{3^2} \times {2^2} \times 2} \\
   \Rightarrow \sqrt {72} = 6\sqrt 2 \\
 \]
Step 2: Now, we have to solve the first term of the expression which is $\sqrt {800} $ with the help of the formula (1) as mentioned in the solution hint.
$ \Rightarrow \sqrt {800} = \sqrt {100 \times 8} $
Now, again we will try to make squares of the terms inside the square root.
$
   \Rightarrow \sqrt {800} = \sqrt {{{10}^2} \times {2^2} \times 2} \\
   \Rightarrow \sqrt {800} = 20\sqrt 2 \\
 $
Step 3: Now, we have to solve the first term of the expression which is \[\sqrt {18} = \sqrt {9 \times 2} \]with the help of the formula (1) as mentioned in the solution hint.
\[ \Rightarrow \sqrt {18} = \sqrt {9 \times 2} \]
Now, again we will try to make squares of the terms inside the square root.
$
   \Rightarrow \sqrt {18} = \sqrt {{3^2} \times 2} \\
   \Rightarrow \sqrt {18} = 3\sqrt 2 \\
 $
Step 4: Now, we have to substitute all the values obtained from the step 1, 2, and 3 in the expression (1) to find the solution of the expression.
$
   = 6\sqrt 2 + 20\sqrt 2 - 3\sqrt 2 \\
   = 26\sqrt 2 - 3\sqrt 2 \\
   = 23\sqrt 2 \\
 $

Hence, with the help of the formula (1) and solving all the terms separately we have obtained value of the given expression: $\sqrt {72} + \sqrt {800} - \sqrt {18} = 23\sqrt 2 $.

Note:
It is easy to solve expressions by finding the values of all it’s parts separately and after finding the values of all the terms we can substitute the terms in the expression to solve it.
To solve the given expression we must follow the BODMAS (Brackets, Divide, Multiply, Addition, Subtraction) rule to find the correct value of the given expression.