Question

expressions
20 100%
√72x
?

Explanation:

Step1: Factor the radicand

We factor 72 into its prime factors. We know that \(72 = 36\times2\), and 36 is a perfect square (\(36 = 6^{2}\)). So we can rewrite the radicand \(72x\) as \(36\times2x\).

$$ \sqrt{72x}=\sqrt{36\times2x} $$

Step2: Apply the square - root property

Using the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a\geq0\) and \(b\geq0\)), we can split the square root of the product into the product of square roots.

$$ \sqrt{36\times2x}=\sqrt{36}\times\sqrt{2x} $$

Since \(\sqrt{36} = 6\) (because \(6^{2}=36\)), we substitute this value back into the expression.

$$ \sqrt{36}\times\sqrt{2x}=6\sqrt{2x} $$

Answer:

\(6\sqrt{2x}\)