Question

How do you simplify the square root of 7 plus by the square root of 7 divided by 2?

Answer 1

Hint:
In this question we have to simplify the expression which is given in phrase, first convert the given phrase into mathematical expression, then simplify the expression according to the given operations in the given phrase, here we have to add the square root of 7 and $\dfrac{{\sqrt 7 }}{2}$, then further simplifying the expression we will get the required answer.

Complete step by step solution:
Given statement is square root of 7 plus by the square root of 7 divided by 2,
Now rewriting the statement in mathematical expression, we get,
First is square root of 7, this can be written as, $\sqrt 7 $,
And second statement is the square root of 7 divided by 2, and this can be written as $\dfrac{{\sqrt 7 }}{2}$,
Now the complete statement will become,
$ \Rightarrow \sqrt 7 + \dfrac{{\sqrt 7 }}{2}$,
Now taking L.C.M get a common denominator, we get,
$ \Rightarrow \dfrac{{\sqrt 7 \times 2}}{2} + \dfrac{{\sqrt 7 }}{2}$,
Now simplifying we get,
$ \Rightarrow \dfrac{{2\sqrt 7 }}{2} + \dfrac{{\sqrt 7 }}{2}$,
Now we can add the two terms as their denominators are equal and to add and subtract radicals, they must be the same radical, then we get,
$ \Rightarrow \dfrac{{2\sqrt 7 + \sqrt 7 }}{2}$,
Now simplifying we get,
$ \Rightarrow \dfrac{{3\sqrt 7 }}{2}$,
So, the simplified term is $\dfrac{{3\sqrt 7 }}{2}$.

$\therefore $The simplified term of the phrase square root of 7 plus by the square root of 7 divided by 2 will be equal to $\dfrac{{3\sqrt 7 }}{2}$.

Note:
A radical can be defined as a symbol that indicates the root of a number. Square root, cube root, fourth root are some of the radicals. As the radicals are actually exponential expressions, they follow the rules of exponents and cannot be added together. In particular, we should avoid the common mistake shown below:
$\sqrt {a + b} \ne \sqrt a + \sqrt b $,
This means that when we are dealing with radicals with different radicands, like $\sqrt 5 $ and $\sqrt 7 $there is really no way to combine or simplify them. However, when dealing with radicals that share a base, we can simplify them by combining like terms.