Question

__ What is √68 in simplest radical form?

Answer 1

The simplest radical form is $2 \sqrt{17}$

Explanation:

The expression is $\sqrt{68}$

To determine the radical form, let us write the number 68 as a product of prime factors.

Thus, we have,

$\sqrt{68} =\sqrt{2\times2\times17}$

Since, 2, 17 are prime factors and hence, no further factorization is possible.

Hence, it can be written as,

$\sqrt{68} =\sqrt{2^{2} \times17}$

Applying the radical rule $\sqrt{a b}=\sqrt{a} \ \sqrt{b}$, we have,

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

Simplifying, we have,

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

Thus, the simplest radical form is $2 \sqrt{17}$