Question

I need some help, I'm still having trouble multiplying radical terms.

Answer 1

$\sqrt[]{a}=a^{\frac{1}{2}}$

$\sqrt[3]{a}=a^{\frac{1}{2}}$

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Areas

smaller rectangle= side 1 * side 2

=5 √2 * 3

= (5*3)√2

= 15 √2 in^2

(in this case, I multiply just the integers I only indicated the radical number)

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bigger rectangle = side 1 * side 2

=5 √2 * 3 √2

= 5 * 3 * (√2* √2)

= 15 * √ (2* 2) (I can rearrange the terms and I include the two radicals in one because they have the same index )

= 15 √ (2^2)

= 15 *2

= 30 in^2

(this is a different case because we have √2* √2 and both have the same index )

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Entire rectangle = smaller rectangle + bigger rectangle

= 30 + 15 √2

or

= 15 (2 + √2 )

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Answer

The area 1 is 15 √2 in^2

The area 2 is 30 in^2

The area of the entire rectangle is = 30 + 15 √2 in^2