Question

What is the simplest form of square root 64x^16

Answer 1

Rewrite 64x1664x16 as (8x8)28x82.√(8x8)28x82Pull terms out from under the radical, assuming positive real numbers.

`8 x^(8)`

Answer 2

`8x^8`

Explanation:

Given:
`√(64x^4)`

This can be written as:
`√(64)`
`\sqrt{x^(16) }`

√64 is the perfect square number.

√64 =
`√(8^2)`

Here the square and square root will get cancelled, we get

√64 = 8

Now let's simplify
`\sqrt{x^(16) } = \sqrt{(x^(8)) ^2}` =
`x^(8)`

Using the power of power rule for exponents

`(a^(m))^n = a^(mn)`

Therefore,
`√(64x^16) = √(64) \sqrt{x^(16) } = 8x^8`