Question

Write the sum of 7√28x6+4√7x6 in simplest form, if x≠0

Answer 1

0

Explanation:

7√2(8)(06)+4√7(06)

7√2(8)(06)+4√7(06)

=0

Answer 2

The simplified form of
`\(7√(28x^6) + 4√(7x^6)\)` is
`\(x(14 + 4x)\)`.

To simplify the expression
`\(7√(28x^6) + 4√(7x^6)\)`, you can first factor out any common factors from the radicands (the expressions inside the square roots).

Step 1: Factor out common factors from the radicands.

`\(7√(28x^6)\)` can be simplified as follows:

`\(7√(28x^6) = 7√((4x^2)(7x^4))\)`

Similarly, for
`\(4√(7x^6)\)`, you can factor out the common factors:

`\(4√(7x^6) = 4√((1x^2)(7x^4))\)`

Step 2: Simplify the square roots of the factored expressions.

Now, let's simplify each square root individually:

For
`\(7√((4x^2)(7x^4))\)`, you can split it into two square roots:

`\(7√((4x^2)(7x^4)) = 7√(4x^2) \cdot √(7x^4)\)`

Simplify each square root separately:

`\(7√(4x^2) = 7(2x) = 14x\)`

`\(√(7x^4) = x^2\)`

Similarly, for
`\(4√((1x^2)(7x^4))\)`, you can split it into two square roots:

`\(4√((1x^2)(7x^4)) = 4√(x^2) \cdot √(7x^4)\)`

Simplify each square root separately:

`\(4√(x^2) = 4x\)`

`\(√(7x^4) = x^2\)`

Step 3: Combine the simplified square roots.

Now that both square roots have been simplified, combine them back into a single expression:

`\(14x + 4x^2\)`

Step 4: Factor out the common factor, which is x:

`\(x(14 + 4x)\)`

So, the answer is
`\(x(14 + 4x)\)`.