How do you simplify √75 + √48 ?

To simplify the expression √75 + √48, we first break down each square root into its prime factors.

Breaking Down the Square Roots

Starting with √75:

• 75 can be factored into 25 and 3.
• Since 25 is a perfect square, we have √75 = √(25 × 3) = √25 × √3 = 5√3.

Now, let's simplify √48:

• 48 can be factored into 16 and 3.
• Here, 16 is also a perfect square, so we get √48 = √(16 × 3) = √16 × √3 = 4√3.

Combining the Results

Now we can combine the simplified square roots:

• 5√3 + 4√3 = (5 + 4)√3 = 9√3.

The Final Answer

Thus, the simplified form of √75 + √48 is 9√3.