square root of 2250

Steps to Solve

1. Identify the square root operation

The square root of a number $x$ is a value $y$ such that $y^2 = x$. For the number 2250, we need to find $y$ such that $y^2 = 2250$.

2. Factor the number

To simplify the calculation, we can factor 2250. Breaking it down, we can write:

$$ 2250 = 225 \times 10 $$

Next, we can factor 225 and 10 further:

$$ 225 = 15^2 \quad \text{and} \quad 10 = 2 \times 5 $$

So, we can express 2250 as:

$$ 2250 = 15^2 \times 2 \times 5 $$

3. Apply the square root to the factors

Now we will apply the square root across the product:

$$ \sqrt{2250} = \sqrt{15^2 \times 2 \times 5} $$

We can simplify this using the property of square roots:

$$ \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} $$

This gives us:

$$ \sqrt{2250} = \sqrt{15^2} \times \sqrt{2} \times \sqrt{5} $$

4. Calculate the square roots

Since $\sqrt{15^2} = 15$, we have:

$$ \sqrt{2250} = 15 \times \sqrt{2} \times \sqrt{5} $$

Next, we can combine $\sqrt{2} \times \sqrt{5}$ into $\sqrt{10}$:

$$ \sqrt{2250} = 15 \times \sqrt{10} $$

5. Approximate the value (if required)

If we want an approximate numerical value, we can calculate further. Knowing $\sqrt{10} \approx 3.16$, we multiply:

$$ 15 \times 3.16 \approx 47.4 $$