SIMHCJIHTE: sqrt (4-sqrt (7))cdot sqrt (4+sqrt (7))

To solve the expression \(\sqrt{4 - \sqrt{7}} \cdot \sqrt{4 + \sqrt{7}}\), we can use the property of square roots that states \(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\).<br /><br />First, let's simplify the expression inside the square roots:<br /><br />\[<br />\sqrt{4 - \sqrt{7}} \cdot \sqrt{4 + \sqrt{7}} = \sqrt{(4 - \sqrt{7})(4 + \sqrt{7})}<br />\]<br /><br />Next, we need to simplify the product inside the square root:<br /><br />\[<br />(4 - \sqrt{7})(4 + \sqrt{7}) = 4^2 - (\sqrt{7})^2 = 16 - 7 = 9<br />\]<br /><br />So, we have:<br /><br />\[<br />\sqrt{(4 - \sqrt{7})(4 + \sqrt{7})} = \sqrt{9} = 3<br />\]<br /><br />Therefore, the value of the expression \(\sqrt{4 - \sqrt{7}} \cdot \sqrt{4 + \sqrt{7}}\) is \(3\).