Change all these numbers to entire radicals in order to compare them. Then write them from smallest to largest in their original form.
9T2, 2T6,8T3,4T5,6T2
*pretend the T is a square root sign
9√2 = √(81*2)
2√6 = √(4*6)
8√3 = √(64*3)
4√5 = √(16*5)
6√2 = √(36*2)
I'll let you finish off.
Ty
To change these numbers to entire radicals and compare them, we can simplify the expressions by finding the square root of each number. Here's how you can do it step by step:
1. Simplify the numbers by finding the square root of each term.
- 9T2 = √9 * √(T2) = 3√(T2)
- 2T6 = √2 * √(T6) = √2 * √(6 * 6 * T) = 6√(2T)
- 8T3 = √8 * √(T3) = 2√2 * √(T3) = 2√(2T3)
- 4T5 = √4 * √(T5) = 2√(T5)
- 6T2 = √6 * √(T2) = √6 * √(2 * 2 * T) = 2√(6T)
2. Now that we have transformed each number into entire radicals, we can write them from smallest to largest in their original form:
- 2√(T5)
- 3√(T2)
- 2√(6T)
- 2√(2T3)
- 6√(2T)
So, from smallest to largest, the numbers in their original form are:
2√(T5), 3√(T2), 2√(6T), 2√(2T3), 6√(2T)