How do you simplify 7sqrt3*2sqrt6?

3 Answers
May 7, 2017

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

May 7, 2017

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)

May 7, 2017

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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