# How would I do:

sqrt32a^8b + sqrt50a^16b

Are the exponents 8b and 16b or 8 and 16?

I'll assume they are 8a and 16a

sqrt 32 = sqrt (16*2) = 4 sqrt 2

sqrt 50 = sqrt (25*2) = 5 sqrt 2

sqrt32 a^(3b) + sqrt50a^(2b)

= sqrt2*a^(8b)[4 + 5(a^8b)]

There are many ways to write it, but this is one of the shorter ones)

## To simplify the expression sqrt(32a^8b) + sqrt(50a^16b), we can break it down step by step:

Step 1: Simplify the square roots individually.

- sqrt(32) can be simplified by factoring 32 into 16 * 2, which gives us sqrt(16) * sqrt(2). Since sqrt(16) = 4, the first term simplifies to 4sqrt(2).

- sqrt(50) can be simplified by factoring 50 into 25 * 2, which gives us sqrt(25) * sqrt(2). Since sqrt(25) = 5, the second term simplifies to 5sqrt(2).

Step 2: Combine like terms.

- The first term is 4sqrt(2) and the second term is 5sqrt(2), so the expression becomes 4sqrt(2)a^(8b) + 5sqrt(2)a^(16b).

Step 3: Factor out the common terms.

- Both terms have sqrt(2) as a common factor, so we can factor it out: sqrt(2)(4a^(8b) + 5a^(16b)).

So the simplified form of sqrt(32a^8b) + sqrt(50a^16b) is sqrt(2)(4a^(8b) + 5a^(16b)).