(√42)(√12)?

(√42)(√12)

= 2 (√42)(√3)

= 6 (√14)

= 22.45

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√3 x √14 x √3 x √4 = 3 x √2 x √7 x 2 = 6 √14

sqrt(42) * sqrt(12)

= sqrt(2 * 3 * 7) * sqrt(2^2 * 3)

= (2 * 3) * sqrt(2 * 7)

= 6 sqrt(14). Final.

The product of two roots is the same as the root of the product, so:

√42 * √12

√(42 * 12)

√504

Now to simplify this, we need to find square factors that we can pull out. So starting with the prime factorization:

√(2³ * 3² * 7)

We can pull out a 2² and 3². After factoring those:

√[(2² * 3²)(2 * 7)]

We can now reverse the first step and turn this back into the product of roots:

√(2² * 3²) * √(2 * 7)

We can do this one more time:

√(2²) * √(3²) * √(2 * 7)

Now the square roots of squares simplify, as does the product in the final factor:

2 * 3 √14

6√14

That's your simplified term.