Question

Simplify.
Remove all perfect squares from inside the square root. √112a⁶?

Answer 1

The simplified form of
`√112a⁶ is \( 4a^3√(7) \).`

Step-by-step explanation:

To simplify the expression √112a⁶, we break down 112 into its prime factors:
`\( 112 = 2^4 * 7 \).`

Since we're dealing with a square root, we can pair up the factors inside the square root sign.

The perfect square is
`\( 2^4 = 16 \),` and what remains is
`\( 7a^6 \).`

Now, we can take out the perfect square,
`\( 2^2 = 4 \),` from under the square root.

This leaves us with
`\( 4a^3√(7) \)` as the simplified expression.

The 4 comes out because it represents the square root of the perfect square, and
`\( a^3 \)` remains inside the square root since
`\( a^6 \)` is broken down into
`\( a^3 * a^3 \),` and one
`\( a^3 \)` is left inside.

So, the final answer
`\( 4a^3√(7) \)` is a simplified form of the original expression, removing all perfect squares from inside the square root.

This form is often preferred in mathematical expressions as it is more concise and clearer, providing a more elegant representation of the original expression.