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# How do you add square root 2 plus the square root of 6?

Last updated date: 20th Jun 2024
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Hint: In order to determine the value of the above addition we first have to write it in a mathematical expression as $\sqrt 2 + \sqrt 6$. Since $\sqrt 6$ can be rewritten as $\sqrt 2 \sqrt 3$, put this in the expression and pull out $\sqrt 2$ common. Now the approx. value of $\sqrt 2 = 1.41\,$and $\sqrt 3 = 1.73$ to get the answer.

Complete step by step solution:
We are given some statements, and we have to first convert then into some mathematical expression to apply for any operation.
In order to write any mathematical expression from some words and figures ,we must first find the relationship and the quantities specified .
Here in this question we have to add the two square root terms.
Square root of 2 can be expressed as $\sqrt 2$and similarly square root of 6 as $\sqrt 6$
Let's add both of the terms, we get
$= \sqrt 2 + \sqrt 6$
$\sqrt 6$can be rewritten as $\sqrt 2 \sqrt 3$
$= \sqrt 2 + \sqrt 2 \sqrt 3$
Taking common $\sqrt 2$from both the term, we get
$= \sqrt 2 \left( {1 + \sqrt 3 } \right)$
Now putting $\sqrt 2 = 1.41\,$and $\sqrt 3 = 1.73$approx.
$= 1.41\left( {1 + 1.73} \right) \\ = 1.41\left( {2.73} \right) \\ = 3.8493\,\,\,approx. \\$
Therefore the addition of square root 2 plus the square root of 6 is equal to
$3.8493\,\,\,\,\,\,approx$.

Note:
1.Mathematical equation : A Mathematical equation can be defined as the mathematical statement which contains an equal symbol $=$ in between two algebraic expressions that share the same value. An algebraic expression can contain any number of variables generally we take 2-3 variables. Let assume an expression
$5x + 9 = 24$
It is a mathematical equation having LHS (Left-Hand-Side) equal to RHS (Right-Hand-Side)
Where $x$ is the variable 5 is the coefficient of variable $x$ And $24,9$ are the constants
2.$2x + 98 + 78y$ is not a mathematical equation because it does not contain equality $=$ symbol . It is only a mathematical expression.
3. Read the statement carefully in order to convert them into mathematical expressions.