Question

For each of the fractions below, rationalize the denominator and reduce any fractions if possible. Enter a fraction (perhaps involving a square root in the numerator), and not a decimal value.15/8√3=√2/√11=2√10/3√7=

Answer 1

It is important to know that rationalize means to multiply and divide by the same root.

(a)
`\frac{15}{8\sqrt[]{3}}\cdot\frac{\sqrt[]{3}}{\sqrt[]{3}}=\frac{15\sqrt[]{3}}{8\cdot3}=\frac{5\sqrt[]{3}}{8}`(b)
`\frac{\sqrt[]{2}}{\sqrt[]{11}}\cdot\frac{\sqrt[]{11}}{\sqrt[]{11}}=\frac{\sqrt[]{2\cdot11}}{11}=\frac{\sqrt[]{22}}{11}`(c)
`\frac{2\sqrt[]{10}}{3\sqrt[]{7}}\cdot\frac{\sqrt[]{7}}{\sqrt[]{7}}=\frac{2\sqrt[]{10\cdot7}}{3\cdot7}=\frac{2\sqrt[]{70}}{21}`