\( 1.10 \sqrt{20 a^{4} b^{3}} \) \( 1.13 \sqrt[3]{x^{11} y^{7}} \) \( 1.8 \sqrt[3]{96} \) \( 1.11 \sqrt{2^{17} a^{14} b^{13}} \) \( 1.15 \sqrt[3]{3^{2012}} \)

Did you know that the square root and cube root functions have been used since ancient times? The Babylonians had methods for calculating square roots around 2000 BCE, and their techniques were surprisingly similar to the methods we use today! It’s a testament to how effectively they understood mathematics without modern tools. If you're ever getting tangled up with roots, a good habit is to simplify your expressions step by step. For square roots, factor the number into perfect squares and for cube roots, look for perfect cubes. A common mistake is trying to simplify before fully breaking down the expression, which can lead to errors. Break it down, and you'll find it’s much easier to manage!