sqrt32x + 3sqrt8x help please !

sqrt (32x) can also be written

sqrt(4*8x) = 2 sqrt(8x)
That is easily added to 3 sqrt(8x)

sqrt32x + 3sqrt8x

To simplify the expression sqrt(32x) + 3sqrt(8x), we can start by factoring out the perfect squares from under the square roots.

For sqrt(32x), we can rewrite it as sqrt(16 * 2x), since 16 is a perfect square. Using the property of square roots, we can split it into two separate square roots: sqrt(16) * sqrt(2x).

The square root of 16 is 4, so sqrt(16) can be simplified to 4. Therefore, sqrt(32x) can be rewritten as 4sqrt(2x).

Now, let's simplify 3sqrt(8x). Again, we can factor out a perfect square from under the square root. sqrt(8x) can be written as sqrt(4 * 2x).

The square root of 4 is 2, so sqrt(4) simplifies to 2, and we have 2sqrt(2x).

Now we have 4sqrt(2x) + 2sqrt(2x).

Since both terms have the same square root, we can combine them. 4sqrt(2x) + 2sqrt(2x) is equal to 6sqrt(2x).

So the simplified expression is 6sqrt(2x).