Question

How do you simplify `7sqrt3*2sqrt6`?

Answer 1

`42sqrt2`

Explanation:

`"using "color(blue)"law of radicals"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(sqrtaxxsqrtbhArrsqrt(axxb))color(white)(2/2)|)))`

`rArr7sqrt3xx2sqrt6`

`=7xx2xxsqrt3xxsqrt6`

`=14xxsqrt(3xx6)`

`=14xxsqrt18`

`["now " sqrt18=sqrt(9xx2)=sqrt9xxsqrt2=3sqrt2]`

`=14xx3sqrt2`

`=42sqrt2`

Answer 2

See a solution process below:

Explanation:

First, we can rewrite this expression as:

`(7 * 2)(sqrt(3) * sqrt(6)) -> 14(sqrt(3) * sqrt(6))`

We can now use this rule for multiplying radicals to continue the simplification:

`sqrt(a) * sqrt(b) = sqrt(a * b)`

`14(sqrt(3) * sqrt(6) => 14 sqrt(3 * 6) => 14sqrt(18)`

We can now use the same rule we used above but in reverse to rewrite this expression as:

`14sqrt(18) => 4sqrt(9 * 2) => 4(sqrt(9) * sqrt(2)) => 14(+-3 * sqrt(2)) =>`

`+-42sqrt(2)`

Answer 3

`sqrt(a.b) = sqrta.sqrtb`

so, `sqrt6 = sqrt3.sqrt2`

Then, `7sqrt3.(2sqrt6) = 7sqrt3.(2sqrt3).sqrt2`

i.e. `14(3).sqrt2`

so, `42sqrt2`

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