Simplify the Radical Expression square root of (x+15)^4

$\sqrt{{(x + 15)}^{4}}$

Step 1

Rewrite ${(x + 15)}^{4}$ as ${({(x + 15)}^{2})}^{2}$ .

$\sqrt{{({(x + 15)}^{2})}^{2}}$

Step 2

Pull terms out from under the radical.

$| {(x + 15)}^{2} |$

Step 3

Rewrite ${(x + 15)}^{2}$ as $(x + 15) (x + 15)$ .

$| (x + 15) (x + 15) |$

Step 4

Expand $(x + 15) (x + 15)$ using the FOIL Method.

Apply the distributive property.

$| x (x + 15) + 15 (x + 15) |$

Apply the distributive property.

$| x \cdot x + x \cdot 15 + 15 (x + 15) |$

Apply the distributive property.

$| x \cdot x + x \cdot 15 + 15 x + 15 \cdot 15 |$

Step 5

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$| x^{2} + x \cdot 15 + 15 x + 15 \cdot 15 |$

Move $15$ to the left of $x$ .

$| x^{2} + 15 \cdot x + 15 x + 15 \cdot 15 |$

Multiply $15$ by $15$ .

$| x^{2} + 15 x + 15 x + 225 |$

Add $15 x$ and $15 x$ .

$| x^{2} + 30 x + 225 |$