Pergunta

19) (1 Point):Once completely simp! sqrt ((25)/(6)) will be in the form (asqrt (b))/(c) the value for b? __
Solução

4.6285 Voting

EdinaldoProfissional · Tutor por 6 anos
Responder
To simplify the expression \(\sqrt{\frac{25}{6}}\), we can rewrite it as:<br /><br />\[<br />\sqrt{\frac{25}{6}} = \frac{\sqrt{25}}{\sqrt{6}}<br />\]<br /><br />We know that \(\sqrt{25} = 5\), so the expression becomes:<br /><br />\[<br />\frac{5}{\sqrt{6}}<br />\]<br /><br />To rationalize the denominator, we multiply the numerator and the denominator by \(\sqrt{6}\):<br /><br />\[<br />\frac{5}{\sqrt{6}} \times \frac{\sqrt{6}}{\sqrt{6}} = \frac{5\sqrt{6}}{6}<br />\]<br /><br />Thus, the expression \(\sqrt{\frac{25}{6}}\) simplifies to \(\frac{5\sqrt{6}}{6}\).<br /><br />In the form \(\frac{a\sqrt{b}}{c}\), we have \(a = 5\), \(b = 6\), and \(c = 6\).<br /><br />Therefore, the value for \(b\) is:<br /><br />\[<br />\boxed{6}<br />\]
Clique para avaliar: