Question

simplify.
√245

Explanation:

To simplify \(\sqrt{245}\), we start by factoring the radicand (the number inside the square root) into its prime factors.

Step 1: Prime Factorization of 245

We factor 245:
\(245 = 49 \times 5\) (since \(49 \times 5 = 245\)).

Notice that 49 is a perfect square: \(49 = 7^2\).

Step 2: Apply the Square Root Property

Recall the property of square roots: \(\sqrt{ab} = \sqrt{a} \times \sqrt{b}\) (for \(a \geq 0, b \geq 0\)).

Applying this to \(\sqrt{245}\):

$$ \sqrt{245} = \sqrt{49 \times 5} = \sqrt{49} \times \sqrt{5} $$

Since \(\sqrt{49} = 7\) (because \(7^2 = 49\)), we substitute that in:

$$ \sqrt{49} \times \sqrt{5} = 7 \times \sqrt{5} = 7\sqrt{5} $$

So, the simplified form of \(\sqrt{245}\) is \(7\sqrt{5}\).

Answer:

To simplify \(\sqrt{245}\), we start by factoring the radicand (the number inside the square root) into its prime factors.

Step 1: Prime Factorization of 245

We factor 245:
\(245 = 49 \times 5\) (since \(49 \times 5 = 245\)).

Notice that 49 is a perfect square: \(49 = 7^2\).

Step 2: Apply the Square Root Property

Recall the property of square roots: \(\sqrt{ab} = \sqrt{a} \times \sqrt{b}\) (for \(a \geq 0, b \geq 0\)).

Applying this to \(\sqrt{245}\):

$$ \sqrt{245} = \sqrt{49 \times 5} = \sqrt{49} \times \sqrt{5} $$

Since \(\sqrt{49} = 7\) (because \(7^2 = 49\)), we substitute that in:

$$ \sqrt{49} \times \sqrt{5} = 7 \times \sqrt{5} = 7\sqrt{5} $$

So, the simplified form of \(\sqrt{245}\) is \(7\sqrt{5}\).