Question

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

Answer 1

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

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

The simplified expression is:

`54√(2)\cdot x^3y^4`

Explanation:

We are asked to find the expression:

`3x√(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:

`√(4)=√(2* 2)=2` )

Hence, on prime factorizing we get:

`648x^4y^8=2* 2* 2* 3* 3* 3* 3* x* x* x* x* y* y* y* y* y* y * y* y\\\\\\648x^4y^8=(2* 2)* 2* (3* 3)* (3* 3)* (x* x)* (x* x)* (y* y)* (y* y)* (y* y) * (y* y)\\\\i.e.\\\\√(648x^4y^8)=2* 3* 3* x* x* y* y* y* y* √(2)\\\\\\√(648x^4y^8)=18x^2y^4√(2)`

Hence, we get:

`3x√(648x^4y^8)=3x* 18x^2y^4√(2)\\\\i.e.\\\\3x√(648x^4y^8)=54√(2)\cdot x^3y^4`