Question

Simplify: $5\sqrt{8}+2\sqrt{32}-2\sqrt{2}$(approx.).
$\left( A \right)\text{ 21}\text{.6 }$
$\left( B \right)\text{ 22}\text{.6 }$
$\left( C \right)\text{ 22}\text{.9}$
$\left( D \right)\text{ 21}\text{.9}$

Answer 1

Hint: In this question we have been given with an expression which is in the radical form. We will solve this expression by simplifying the roots given in the question and multiplying the terms. we will write the terms inside the root as a multiple of $2$ and when there are two instances of the same number, we will remove it out of the square root. We will then substitute the value of $\sqrt{2}$ as $1.414$ and then multiply to get the required solution.

Complete step-by-step answer:
We have the expression given to us as:
$= 5\sqrt{8}+2\sqrt{32}-2\sqrt{2}\to \left( 1 \right)$
We have to simplify the terms in the square root. Consider the terms $\sqrt{8}$. We can write it as:
$= \sqrt{8}$
Now we can write the number $8$ as a multiple of $2\times 2\times 2$ therefore, on substituting, we get:
$= \sqrt{2\times 2\times 2}$
Now since there two instances of the number $2$, we can remove it out of the root and write it as:
$= 2\sqrt{2}\to \left( 2 \right)$
Consider the terms $\sqrt{32}$. We can write it as:
$= \sqrt{32}$
Now we can write the number $32$ as a multiple of $4\times 4\times 2$ therefore, on substituting, we get:
$= \sqrt{4\times 4\times 2}$
Now since there two instances of the number $4$, we can remove it out of the root and write it as:
$= 4\sqrt{2}\to \left( 3 \right)$
On substituting $\left( 2 \right)$ and $\left( 3 \right)$ in $\left( 1 \right)$, we get:
$= 5\left( 2\sqrt{2} \right)+2\left( 4\sqrt{2} \right)-2\sqrt{2}$
On multiplying the terms, we get:
$= 10\sqrt{2}+8\sqrt{2}-2\sqrt{2}$
Now taking the term $\sqrt{2}$ common from the terms, we get:
$= \sqrt{2}\left( 10+8-2 \right)$
On simplifying, we get:
$= \sqrt{2}\left( 16 \right)$
Now we know that $\sqrt{2}=1.414$ therefore, on substituting, we get:
$= 1.414\times 16$
On multiplying, we get:
$= 22.624\approx 22.6$, which is the required solution therefore, the correct answer is option $\left( B \right)$.

So, the correct answer is “Option B”.

Note: The way to multiply two roots should be remember while doing these types of sums. It is to be remembered that during calculation the term inside the root should not become negative. Perfect squares of numbers should be remembered and the value of $\sqrt{3}=1.732$ can also be required for substitution.