Question

What’s the square root of 50 plus the square root of 32?

Answer 1

Hint:In order to solve this question first, we write the given expression in a mathematical expression. Then we assume a variable equal to the obtained expression. Then we split those terms as multiple of two numbers such that one of them is a perfect square and another is any number. Then take out that number from the square root. And take common and add that number in order to get the final answer.


Complete step by step answer:
First, we express the given expression in mathematical expressions.
Square root of 50 plus square root of 32 \[ = \sqrt {50} + \sqrt {32} \]
Let, the value of the given expression is \[x\].
\[x = \sqrt {50} + \sqrt {32} \]
Now split this into a part such that one part of these is a perfect square and another is any number.
50 can be split as a multiple of 25 and 2. Here, 25 is the perfect square of 5.
32 can be split as a multiple of 16 and 2. Here, 16 is the perfect square of 4.
\[x = \sqrt {25 \times 2} + \sqrt {16 \times 2} \]
Now separate each term.
\[x = \sqrt {25} \times \sqrt 2 + \sqrt {16} \times \sqrt 2 \]
Putting the value of the perfect square root.
\[x = 5\sqrt 2 + 4\sqrt 2 \]
Here \[\sqrt 2 \] is common in both the terms.
\[x = \left( {5 + 4} \right)\sqrt 2 \]
On simplifying the equation.
\[x = 9\sqrt 2 \]
The value of the expression square root of 50 plus square root of 32 is-
\[ \Rightarrow x = 9\sqrt 2 \]

Note: Although this question is easy, to solve this type of question students must be able to understand the language of the question. There is very little possibility of making a mistake. To increase the difficulty level they use different powers to different-different terms. Then simply with the same power terms and with different power, we left separately.