Question

Combine the following expressions:

Answer 1

Answer:

Option B is Correct

Step-by-step explanation:

$\sqrt{48n^3}+\sqrt{9n} - \sqrt{3n}$

We need to solve the above expression.

48 can be written as: 2x2x2x2x3

9 can be written as : 3x3

Putting values

$\sqrt{2*2*2*2*3*n*n*n} +\sqrt{3*3*n}-\sqrt{3n}$

2*2 = 2^2 and n*n = n^2 and 3*3 = 3^2

we also know √ = 1/2

so, putting these values we get,

$\sqrt{2^2*2^2*3*n^2*n} +\sqrt{3^2*n}-\sqrt{3n}\\(2^2)^{1/2} * (2^2)^{1/2} * (3)^{1/2} * (n^2)^{1/2} * n ^{1/2} + ((3^2)^{1/2} *n^{1/2}) -(\sqrt{3n})\\2*2*n * (3^{1/2} *n ^{1/2}) +(3 +n^{1/2}) -(\sqrt{3n})\\4n (\sqrt{3n})+(3 \sqrt{n}) -(\sqrt{3n})\\Rearraninging\\4n(\sqrt{3n}) - (\sqrt{3n})+(3 \sqrt{n})\\Taking \,\,\sqrt{3n} \,\,common\,\, from\,\, 1st\,\, and\,\, 2nd\,\, term\\\sqrt{3n}(4n-1)+(3 \sqrt{n})\\or \,\,it\,\,can\,\,be\,\,written\,\,as\,\,\\(4n-1)\sqrt{3n}+(3 \sqrt{n})$

So, Option B is Correct.

Answer 2

ANSWER

$(4n - 1)\sqrt{3 n} + 3\sqrt{n}$

EXPLANATION

The given expression is

$\sqrt{48 {n}^{3} } + \sqrt{9n} - \sqrt{3n}$

We remove the perfect squares under the radical sign.

$\sqrt{16 {n}^{2} \times3 n} + \sqrt{9n} - \sqrt{3n}$

We can now take square root of the perfect squares and simplify them further.

$\sqrt{16 {n}^{2}} \times \sqrt{3 n} + \sqrt{9} \times \sqrt{n} - \sqrt{3n}$

This simplifies to:

$4n\sqrt{3 n} + 3\sqrt{n} - \sqrt{3n}$

This further simplifies to:

$(4n - 1)\sqrt{3 n} + 3\sqrt{n}$