Simplify $$ \sqrt{75} $$ to the form $$ a \sqrt{b} $$, $$ \sqrt{75}=\square $$ Question Help: Video

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To simplify $$ \sqrt{75} $$ into the form $$ a\sqrt{b} $$, follow these steps:

1. **Factor the Number Under the Square Root:**
   
   Start by finding the largest perfect square that divides 75.

$$
   75 = 25 \times 3
   $$

2. **Apply the Square Root Property:**
   
   The square root of a product is the product of the square roots.

$$
   \sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3}
   $$

3. **Simplify the Square Roots:**
   
   - $$ \sqrt{25} = 5 $$ (since 5 × 5 = 25)
   - $$ \sqrt{3} $$ remains as is because 3 is a prime number and cannot be simplified further.

$$
   \sqrt{75} = 5 \times \sqrt{3} = 5\sqrt{3}
   $$

**Final Answer:**

$$
\sqrt{75} = 5\sqrt{3}
$$
$$ \sqrt{75} = 5\sqrt{3} $$

Simplify \( \sqrt{75} \) to the form \( a \sqrt{b} \), \( \sqrt{75}=\square \) Question Help: Video

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