Method 1: Using fractions
1. Convert 1.5 to a fraction: 1.5 = 3/2.
2. Square the fraction: (3/2)² = (3/2) × (3/2).
3. Multiply the numerators: 3 × 3 = 9.
4. Multiply the denominators: 2 × 2 = 4.
5. The result is 9/4.
6. Convert back to a decimal: 9 ÷ 4 = 2 with a remainder of 1, so 2 and 1/4, which is 2.25.
Method 2: Using multiplication
1. Calculate 1.5 × 1.5. It's easier to calculate 15 × 15 first.
2. 15 × 15 = 225. (You might know this, or calculate it: 15x10=150, 15x5=75, 150+75=225).
3. Now, place the decimal point. The original numbers (1.5 and 1.5) have one decimal place each, so the answer must have 1 + 1 = 2 decimal places.
4. So, 225 becomes 2.25.
Full Answer
2.25
The expression 1.5² means 1.5 multiplied by itself: 1.5 × 1.5. There are a couple of ways to do this without a calculator.
**Method 1: Treat as whole numbers and adjust decimal places**
1. Ignore the decimal points and multiply 15 by 15.
15 × 15 = 225.
2. Count the total number of decimal places in the original numbers. 1.5 has one decimal place, and we are multiplying it by 1.5 which also has one decimal place. Total decimal places = 1 + 1 = 2.
3. Place the decimal point in the result (225) so that it has 2 decimal places. This gives 2.25.
**Method 2: Using fractions**
1. Convert the decimal to a fraction. 1.5 is the same as 1 and a half, which is the improper fraction 3/2.
2. Now square the fraction: (3/2)² = (3/2) × (3/2).
3. To multiply fractions, multiply the numerators and multiply the denominators: (3 × 3) / (2 × 2) = 9/4.
4. Convert the fraction 9/4 back to a decimal. 9 ÷ 4 = 2.25.
Both methods give the answer 2.25.
Common mistakes
✗ Calculating 1.5 x 2 = 3. Squaring is not multiplying by 2.\n✗ Misplacing the decimal point, e.g., getting 22.5 or 0.225.
Expert