Square root of 68 in radical form.

Understand the Problem

The question is asking for the square root of the number 68 presented in its simplest radical form. This involves simplifying the square root by factoring 68 into its prime factors and reducing the radical if possible.

Answer

$2\sqrt{17}$

Steps to Solve

Factor the Number

First, we need to find the prime factorization of 68. We can divide 68 by the smallest prime number, which is 2.

$$ 68 \div 2 = 34 $$

Next, we can factor 34:

$$ 34 \div 2 = 17 $$

Now, we have:

$$ 68 = 2^2 \times 17 $$

Apply the Square Root Property

Using the property of square roots, we can separate the square root into the product of the square roots of the factors:

$$ \sqrt{68} = \sqrt{2^2 \times 17} $$

Simplify the Square Root

Now we can simplify this further by applying the square root to (2^2):

$$ \sqrt{68} = \sqrt{2^2} \times \sqrt{17} = 2\sqrt{17} $$

The simplest radical form of the square root of 68 is $2\sqrt{17}$.

More Information

In mathematics, the process of simplifying square roots is a common technique. By factoring numbers into their prime components, we can often reduce expressions into simpler forms.

Tips

Misidentifying the prime factors of a number, leading to incorrect simplification.
Forgetting to separate the square root into its factors before simplifying.
Not recognizing numbers that can be simplified (e.g., $2^2$ in this case).

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