Question

help with radical expressions please 3/sqrt7 and 3/2- sqrt7

Answer 1

If you've got just one radical for the denominator, you can rationalize the expression by multiplying both numerator and denominator by the denominator. For example, \[\frac{1}{\sqrt{5}} = \frac{1}{\sqrt{5}} * \frac{\sqrt{5}}{\sqrt{5}} = \frac{\sqrt{5}}{5}\]

If you have something where there are two terms in the denominator, and one or more of them feature a radical sign, you can multiply both numerator and denominator by the conjugate of the denominator. For example, \[\frac{1}{1-\sqrt{2}} = \frac{1}{1-\sqrt{2}}*\frac{1+\sqrt{2}}{1+\sqrt{2}} = \frac{1+\sqrt{2}}{1-2} = -1-\sqrt{2}\]

You construct the conjugate by changing the sign in the middle. You're taking advantage of the property of a difference of squares:\[(a+b)(a-b) = a^2-ab+ab-b^2 = a^2-b^2\]Squaring both terms clears away the radicals.