Question

Which is equivalent to V180x11 after it has been simplified completely?

© 3x10653



O 3x® v5x



O 6x10/5x



O 6x55x

Answer 1

D on edg

Explanation:

6x^5 V5x is correct

Answer 2

Question:

Which is equivalent to
`\sqrt{180x^(11)}` after it has been simplified completely?

Answer:

`\sqrt{180x^(11)} = 6x^(5)√(5x)`

Explanation:

Given

`\sqrt{180x^(11)}`

Required

Simplify

We start by splitting the square root

`\sqrt{180x^(11)} = √(180) * \sqrt{x^(11)}`

Replace 180 with 36 * 5

`\sqrt{180x^(11)} = √(36 * 5) * \sqrt{x^(11)}`

Further split the square roots

`\sqrt{180x^(11)} = √(36) *√(5) * \sqrt{x^(11)}`

`\sqrt{180x^(11)} = 6*√(5) * \sqrt{x^(11)}`

Replace power of x; 11 with 10 + 1

`\sqrt{180x^(11)} = 6*√(5) * \sqrt{x^(10 + 1)}`

From laws of indices;
`a^(m+n) = a^m * a^n`

So, we have

`\sqrt{180x^(11)} = 6*√(5) * \sqrt{x^(10) * x^1}`

`\sqrt{180x^(11)} = 6*√(5) * \sqrt{x^(10) * x}`

Further split the square roots

`\sqrt{180x^(11)} = 6*√(5) * \sqrt{x^(10)} * √(x)`

From laws of indices;
`√(a) = a^{(1)/(2)}`

So, we have

`\sqrt{180x^(11)} = 6*√(5) * x^{10*(1)/(2)} * √(x)`

`\sqrt{180x^(11)} = 6*√(5) * x^{(10)/(2)} * √(x)`

`\sqrt{180x^(11)} = 6*√(5) * x^(5) * √(x)`

Rearrange Expression

`\sqrt{180x^(11)} = 6 * x^(5) * √(5) * √(x)`

`\sqrt{180x^(11)} = 6x^(5) * √(5) * √(x)`

From laws of indices;
`√(a) *√(b) = √(a*b) = √(ab)`

So, we have

`\sqrt{180x^(11)} = 6x^(5) * √(5*x)`

`\sqrt{180x^(11)} = 6x^(5) * √(5x)`

`\sqrt{180x^(11)} = 6x^(5)√(5x)`

The expression can no longer be simplified

Hence,
`\sqrt{180x^(11)}` is equivalent to
`6x^(5)√(5x)`