Question

Simplify the expression. 3x square root of 648x^4y^8

Answer 1

Answer: 3x sq. root of 648^x*2^3+2y

Step-by-step explanation:

3x square root of 648x^4y^8

you do something to the 4 and eight

math is complicated and your teacher will most likely not check it

as long as it looks intelligible

4/8 = 2

idk

there's the possibility that the expression cant be simplified

Answer 2

Answer:

The simplified expression is:

              $54\sqrt{2}\cdot x^3y^4$

Step-by-step explanation:

We are asked to find the expression:

             $3x\sqrt{648x^4y^8}$

We know that if any quantity under the square root sign  is doubled then it comes out of the radical sign as one.

(  for example:

$\sqrt{4}=\sqrt{2\times 2}=2$  )

Hence, on prime factorizing we get:

$648x^4y^8=2\times 2\times 2\times 3\times 3\times 3\times 3\times x\times x\times x\times x\times y\times y\times y\times y\times y\times y \times y\times y\\\\\\648x^4y^8=(2\times 2)\times 2\times (3\times 3)\times (3\times 3)\times (x\times x)\times (x\times x)\times (y\times y)\times (y\times y)\times (y\times y) \times (y\times y)\\\\i.e.\\\\\sqrt{648x^4y^8}=2\times 3\times 3\times x\times x\times y\times y\times y\times y\times \sqrt{2}\\\\\\\sqrt{648x^4y^8}=18x^2y^4\sqrt{2}$

Hence, we get:

$3x\sqrt{648x^4y^8}=3x\times 18x^2y^4\sqrt{2}\\\\i.e.\\\\3x\sqrt{648x^4y^8}=54\sqrt{2}\cdot x^3y^4$