Question

Solve:$8\sqrt {28} \div 2\sqrt 7 $
$\left( A \right)8$
$\left( B \right)4$
$\left( C \right)2$
$\left( D \right)16$

Answer 1

Hint: Here given the problem of division of roots. This question is based on simple operations while using basic formula,
$ = \sqrt {a \times b} = \sqrt a \times \sqrt b $_ _ _ _ _ _ _ _ _ _ $\left( 1 \right)$
$ = $ Set up this type of problem in fractions. This makes it easier to follow steps using formula.
$ = $Factorize the number given in the roots as much as possible to find the square root, this will make the problem easier to solve.

Complete step-by-step answer:
Given question is $8\sqrt {28} \div 2\sqrt 7 $ a simple division of roots.
We can write this as,
$ = \dfrac{{8\sqrt {27} }}{{2\sqrt 7 }}$
We can write $\sqrt {27} $as$\sqrt {4 \times 7} $.
So, it becomes,
$ = \dfrac{{8\sqrt {4 \times 7} }}{{2\sqrt 7 }}$
By using $\left( 1 \right)$,
$ = \dfrac{{8\sqrt 4 \times \sqrt 7 }}{{2\sqrt 7 }}$
Value of $\sqrt 4 $is $2$.
$ = \dfrac{{8 \times 2\sqrt 7 }}{{2\sqrt 7 }}$
$ = \dfrac{{16\sqrt 7 }}{{2\sqrt 7 }}$
Here, Numerator$\sqrt 7 $ denominator$\sqrt 7 $ gets cancelled.
$ = \dfrac{{16}}{2}$
$ = 8$.
Therefore, $\left( A \right)8$ is the final answer of the question.

So, the correct answer is “Option A”.

Note: $ = $Here given the problem of division of roots. We know while doing division of roots their power must be the same, no matter whatever the number will be there. For any Number Power must be the same as a numerator same as a denominator.
So, while solving this type of problem we have to do the first step that is to equalize the power of the numerator and denominator.
$ = $If there is no square root present in the numerator, but the denominator has the root, then there is the method called Rationalizing the denominator.