What is a square of 75?

What is the square root of 75?

When we talk about the "square" of a number, we usually mean multiplying it by itself. But in this case, the question is really asking how to turn 75 into a perfect square—a number that’s the square of a whole number.

Here’s where number sense comes in. The number 75 breaks down into prime factors: 5 × 5 × 3. We can already see that 5 appears twice, forming a pair—but 3 stands alone. For a number to be a perfect square, all prime factors must come in pairs. Since 3 is unpaired, 75 isn’t a perfect square on its own.

So, what do we do? Multiply 75 by 3. That gives us 225, and now the prime factors are 5 × 5 × 3 × 3, everything is paired up. That means 225 is a perfect square. And sure enough, the square root of 225 is 15, because 15 × 15 = 225.

In other words, you can’t make 75 a perfect square by squaring it, rather, you make it one by multiplying it by the missing piece: 3. It’s a small but clever trick rooted in prime factorization, something often overlooked in basic math but incredibly useful when simplifying radicals or solving algebraic problems.

So while 75 itself isn’t a perfect square, with just a little adjustment, it leads us to 225, a clean, neat square that makes everything balance. Math, after all, is often about finding the missing piece that brings harmony to the equation.