Question

How do you simplify \[2\] times the square root of \[20?\]

Answer 1

Hint: The given question involves the arithmetic operations of addition/ subtraction/ multiplication/ division. We need to know the square root values of basic numbers. We need to know the relation between the square root and square functions. Also, we need to know the keyword \[2\] times indicates which operation in the arithmetic functions.

Complete step by step solution:
To solve the given question we would simplify the term \[2\] times the square root of \[20\].
Here \[2\] times means we have to multiply the square root of \[20\] with \[2\]. It can be written as follows,
\[2\sqrt {20} = ? \to \left( 1 \right)\]
First, we have to find the value \[\sqrt {20} \]in the above equation.
We know that,
\[5 \times 4\]\[ = 20\]
So, we get
\[\sqrt {20} = \sqrt {5 \times 4} \]
We know that,
\[{2^2} = 4\]
So, we get
\[\sqrt {20} = \sqrt {5 \times 4} = \sqrt {5 \times {2^2}} \]
In the above equation, the square and square root terms can be canceled by each other. So, we can take the term\[2\]from inside to outside the square root.
So, we get
\[\sqrt {20} = 2\sqrt 5 \to \left( 2 \right)\]
Let’s substitute the equation\[\left( 2 \right)\]in the equation\[\left( 1 \right)\], we get
\[\left( 1 \right) \to 2\sqrt {20} = ?\]
\[2\sqrt {20} = 2 \times 2\sqrt 5 = 4\sqrt 5 \]
\[2\sqrt {20} = 4\sqrt 5 \]
Let’s solve the term\[\sqrt 5 \]as follows,

So, the value of \[\sqrt 5 \] can be written as, \[2.2\]
So, we get
\[2\sqrt {20} = 4 \times \sqrt 5 = 4 \times 2.2\]
\[2\sqrt {20} = 8.8\]
So, the final answer is,
\[2\sqrt {20} = 8.8\]

Note: This question describes the operation of addition/ subtraction/ multiplication/ division. To solve these types of questions we would remember the process of finding square root values with or without using a calculator. If a square term is present inside the square root function we can take it out from the square root. Note that the final answer would be a most simplified form of a given equation or term in the question.