Guess and Check is an important problem-solving strategy. Use guess and check to solve each puzzle. a) A number times itself is 100. What is the number? b) A number times itself is 225. What is the number?

I'll be glad to check your answers.

Hint: find the square roots of 100 and 225.

To solve these puzzles using the guess and check strategy, we systematically guess numbers and check if the condition is satisfied. Let's go through each puzzle step by step:

a) A number times itself is 100. What is the number?
- Start by guessing a number and multiply it by itself to see if it equals 100.
- Let's start with the number 1: 1 * 1 = 1 (not 100)
- Try the number 2: 2 * 2 = 4 (still not 100)
- Continue checking other numbers until we find the number that, when multiplied by itself, equals 100.
- If we try 10, we get: 10 * 10 = 100.
- So, the number is 10.

b) A number times itself is 225. What is the number?
- Follow the same process as before, but starting with different numbers.
- Try the number 1: 1 * 1 = 1 (not 225)
- Try the number 2: 2 * 2 = 4 (still not 225)
- Continue checking other numbers until we find the number that, when multiplied by itself, equals 225.
- If we try 15, we get: 15 * 15 = 225.
- So, the number is 15.

Using the guess and check strategy, we found that the number in both puzzles is 10 and 15, respectively.