Question

8.5 divide radical expressions (homework) score: 5/14 answered: 5/14 question 6 rationalize the denominator: $\frac{4}{3+sqrt{2}}=$ question help: video written example submit question jump to answer

Explanation:

Step1: Multiply by conjugate

Multiply numerator and denominator by $3 - \sqrt{2}$: $\frac{4}{3+\sqrt{2}}\times\frac{3 - \sqrt{2}}{3 - \sqrt{2}}$

Step2: Expand numerator and denominator

Numerator: $4\times(3 - \sqrt{2})=12 - 4\sqrt{2}$. Denominator: $(3+\sqrt{2})(3 - \sqrt{2})=3^{2}-(\sqrt{2})^{2}=9 - 2 = 7$

Answer:

$\frac{12 - 4\sqrt{2}}{7}$