Simplifying radicals, step by step
Simplifying a radical is finding the largest perfect square hidden inside it.
The question
Simplify √75
√75
75 = 25 × 3
√75 = √25 × √3
√75 = 5√3
- Split 75 into a perfect square times whatever is left: 75 = 25 × 3. 25 is 5 squared, and 3 has no square factor of its own — that last part is what makes this the LARGEST perfect square inside, and it is where the answer stops.
- A root splits across a product, so the one root becomes two.
- √25 is 5, so it comes out in front. √3 stays under the sign, because 3 has nothing more to give.
How it works.
- 01
Split 75 into a perfect square times whatever is left: 75 = 25 × 3. 25 is 5 squared, and 3 has no square factor of its own — that last part is what makes this the LARGEST perfect square inside, and it is where the answer stops.
- 02
A root splits across a product, so the one root becomes two.
- 03
√25 is 5, so it comes out in front. √3 stays under the sign, because 3 has nothing more to give.