The nature of roots of equation $x^2-2\sqrt[]{5}x+3=0$ is as follows

<p>Discriminant&nbsp;<math><mrow><mo>=</mo><msup><mrow><mo stretchy="false"> (</mo><mn>2</mn><mroot><mrow><mn>5</mn></mrow><mrow></mrow></mroot><mo stretchy="false">)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mn>4</mn><mo stretchy="false"> (</mo><mn>1</mn><mo stretchy="false">)</mo><mo stretchy="false"> (</mo><mn>3</mn><mo stretchy="false">)</mo><mo>=</mo><mn>2</mn><mn>0</mn><mo>−</mo><mn>1</mn><mn>2</mn><mo>=</mo><mn>8</mn></mrow></math></p><p>So, the roots are real and irrational.</p>

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