Question

Simplify square root 80x^4y^9 to form aVb

Answer 1

Explanation:

sqrt(80x⁴y⁹)

80 = 4×4×5

so, sqrt(80) = 4×sqrt(5)

sqrt(x⁴) = x²

sqrt(y⁹) is ugly. because 9 cannot be divided by 2 as integer result.

we could write it as

sqrt(y⁹) = y^9/2 = y^4.5

so, we either keep it under the square root or we need to do the ugly thing. what does your teacher want ?

so, the result could be either

4x²×sqrt(5y⁹)

a = 4x²

b = 5y⁹

or

4x²y^9/2 × sqrt(5)

a = 4x²y^9/2

b = 5

I personally find the first option the nicer simplification.