Question

foundations of mathematics & pre-calculus 10
chapter 4 – roots and powers

1. sqrt4{625}
2. is 196 is perfect square? why or why not?

if we can not evaluate the root? we can at leas

Explanation:

Problem 3:

Step1: Factorize 625

We know that \( 625 = 5\times5\times5\times5 \), which can be written as \( 5^4 \).

Step2: Simplify the fourth root

The fourth root of \( 5^4 \) is calculated as \( \sqrt[4]{5^4} \). By the property of roots \( \sqrt[n]{a^n}=a \) (when \( a\geq0 \) and \( n \) is a positive integer), so \( \sqrt[4]{5^4}=5 \).

A perfect square is a number that can be expressed as the square of an integer. To check if 196 is a perfect square, we find if there exists an integer \( n \) such that \( n^2 = 196 \). We know that \( 14\times14 = 196 \) (or \( 14^2=196 \)), and 14 is an integer. So 196 is a perfect square because it is the square of the integer 14.

Answer:

\( 5 \)

Problem 4: