Question

Based on the work shown on the left, what is the simplest form of sqrt 250c^3/9d^6?

Answer is A on edge.

Answer 1

`\sqrt{(250c^3)/(9d^6)} = (5√(10c^3) )/(3d^3)`

Explanation:

Given

`\sqrt{(250c^3)/(9d^6)}`

Required

Simplify to the simplest form

We start by splitting the square root

`\sqrt{(250c^3)/(9d^6)} = (√(250c^3))/(√(9d^6))`

Expand

`\sqrt{(250c^3)/(9d^6)} = (√(250 * c^3))/(√(9 * d^6))`

Further Split the square root

`\sqrt{(250c^3)/(9d^6)} = (√(250) * √(c^3))/(√(9)*√(d^6))`

`\sqrt{(250c^3)/(9d^6)} = (√(250) * √(c^3))/(3*√(d^6))`

From laws of indices;

`\sqrt[n]{a^m} = a^{(m)/(n)}`

This implies that

`\sqrt{(250c^3)/(9d^6)} = \frac{√(250) * √(c^3)}{3*{d^{(6)/(2)}}}`

`\sqrt{(250c^3)/(9d^6)} = \frac{√(250) * √(c^3)}{3*{d^3}}`

Expand 250 to 25 * 10

`\sqrt{(250c^3)/(9d^6)} = \frac{√(25 * 10) * √(c^3)}{3*{d^3}}`

`\sqrt{(250c^3)/(9d^6)} = \frac{√(25)*√(10) * √(c^3)}{3*{d^3}}`

`\sqrt{(250c^3)/(9d^6)} = \frac{5*√(10) * √(c^3)}{3*{d^3}}`

Combine the square roots

`\sqrt{(250c^3)/(9d^6)} = \frac{5*√(10*c^3) }{3*{d^3}}`

`\sqrt{(250c^3)/(9d^6)} = (5√(10c^3) )/(3d^3)`

Solved

Answer 2

its a

Explanation:

i just did it