Rose Harrison, Clara Huizink, Aidan Sproat Clements and, Marlene Torres Skoumal Solutions for Exercise 13: Exploration 3

Use the rules of radicals to simplify:

$\sqrt{8}\times \sqrt{2}$

Use the rules of radicals to simplify:

$\frac{\sqrt{8}}{\sqrt{2}}$

Simplify the following by writing $8$ as a power of $2$, and using the rules of exponents:

$8^{\frac{1}{2}}\times 2^{\frac{1}{2}}$

Simplify the following by writing $8$ as a power of $2$, and using the rules of exponents:

$8^{\frac{1}{2}}÷2^{\frac{1}{2}}$

Justify why the two methods, "Rules of exponents and Rules of radicals" for simplifying expressions with square roots are equivalent.

Use the rules of exponents to show that for $a, b\ge 0$, $\sqrt[3]{ab}=\sqrt[3]{a}\times \sqrt[3]{b}$, Generalise your findings.

Use the rules of exponents to show that for $a\ge 0, b>0$, $\sqrt[4]{\frac{a}{b}}=\frac{\sqrt[4]{a}}{\sqrt[4]{b}}$, Generalise your findings.

Use the rules of exponents to show that $\sqrt[n]{a^n}=a$, where$a\ge 0, n>0$.