Question

rewrite the radical expression in its simplified form.\\(\sqrt{98}=\\) type your answer... \\(\sqrt{\text{type your answer...}}\\)

Explanation:

Step1: Factor 98 into prime factors

We know that \(98 = 49\times2\), and \(49 = 7^2\). So, \(98 = 7^2\times2\).

Step2: Apply the square - root property \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) (\(a\geq0,b\geq0\))

According to the property of square roots \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) (\(a\geq0,b\geq0\)), for \(\sqrt{98}=\sqrt{7^{2}\times2}\), we can split it as \(\sqrt{7^{2}}\times\sqrt{2}\).
Since \(\sqrt{7^{2}} = 7\) (because the square root of a perfect square \(x^{2}\) is \(|x|\), and when \(x = 7\), \(\sqrt{7^{2}}=7\)).
So \(\sqrt{98}=7\sqrt{2}\).

Answer:

The first box should be filled with \(7\) and the second box should be filled with \(2\). So \(\sqrt{98}=\boldsymbol{7}\sqrt{\boldsymbol{2}}\)