Question

How do you simplify the square root of \[175\] minus the square root of \[28\]?

Answer 1

Hint:In the given question, we have been given two numbers inside the square root bracket. We have to simplify them by finding their difference. We are first going to simplify the square root bracket – taking out the equal number pairs as a single number. Then we are going to solve them by subtracting them.

Complete step by step answer:
The given expression in algebraic expression is:
\[\sqrt {175} - \sqrt {28} \]
First, we will solve the square root brackets:
Here, we will solve first square root,
\[\sqrt {175} = \sqrt {7 \times 25} = \sqrt {7 \times {{\left( 5 \right)}^2}} = 5\sqrt 7 \]
Now we will solve second square root ,
\[\sqrt {28} = \sqrt {7 \times 4} = \sqrt {7 \times {{\left( 2 \right)}^2}} = 2\sqrt 7 \]
So on simplifying we get, \[\sqrt {175} - \sqrt {28} = 5\sqrt 7 - 2\sqrt 7 = 3\sqrt 7 \]

Hence, the value of the square root of \[175\] minus the square root of \[28\] is \[3\sqrt 7 \].

Additional Information:
We can subtract two square roots only if they have the same number inside the square root bracket. The same thing applies to the operation of addition. But, in the case of multiplication or division, we can multiply or divide any two square root numbers and they are going to be treated as a single number.

Note: In the given question, we were given two numbers inside two different square root brackets. We had to simplify their difference. We did that by first simplifying the square root bracket – taking out the equal number pairs as a single number, and then solving them by subtracting them.