The square root of 1.04 is approximately 1.0198 (rounded to four decimal places). It can be calculated using the approximation method or by converting to a fraction. Since 1.02² = 1.0404, the square root of 1.04 is slightly less than 1.02.
√1.04 ≈ 1.0198 (exact: 1.019803902...).
Approximation method: √(1+0.04) ≈ 1 + 0.04/2 = 1.02.
Fraction method: √1.04 = √(26/25) = √26/5 ≈ 1.0198.
1.02² = 1.0404 (so √1.04 is slightly less than 1.02).
For most exam purposes, √1.04 ≈ 1.02 is sufficient.
1.04 = 104/100 = 26/25 (as a fraction).
√1.04 ≈ 1.0198 (to 4 decimal places)
Verification: 1.0198² = 1.0198 × 1.0198 ≈ 1.03999 ≈ 1.04 ✓
More precisely: √1.04 = 1.019803902...
Rounded values: • To 1 decimal: 1.0 • To 2 decimal: 1.02 • To 3 decimal: 1.020 • To 4 decimal: 1.0198
For small values of x: √(1 + x) ≈ 1 + x/2
Here: 1.04 = 1 + 0.04, so x = 0.04
√1.04 = √(1 + 0.04) ≈ 1 + 0.04/2 = 1 + 0.02 = 1.02
This is a good approximation for exam use: √1.04 ≈ 1.02
This method works well when x is small (x < 0.1).
Convert 1.04 to a fraction: 1.04 = 104/100 = 26/25
√(26/25) = √26 / √25 = √26 / 5
√26 ≈ 5.099 (since 5² = 25, 5.1² = 26.01 ≈ 26)
So √1.04 = 5.099 / 5 = 1.0198
Alternatively: √1.04 = √(104/100) = √104 / 10 √104 = 2√26 ≈ 2 × 5.099 = 10.198 √1.04 = 10.198 / 10 = 1.0198
Using the long division method for square roots:
1.04 = 1.0400
Step 1: √1 = 1, remainder = 0 Step 2: Bring down 04 → 04 Double of quotient = 2; 2_ × _ ≤ 4 → 20 × 0 = 0, try 1: 21 × 1 = 21 > 4. Use 0. So next digit = 0, remainder = 4 Step 3: Bring down 00 → 400 Double of quotient (10) = 20; 20_ × _ ≤ 400 → 201 × 1 = 201, 202 × 2 = 404 > 400. Use 1. Next digit = 1 Wait: 201 × 1 = 201, remainder = 400 − 201 = 199 Step 4: Continue → quotient ≈ 1.019...
Result: √1.04 ≈ 1.0198
The square root of 1.04 is approximately 1.0198. Using the approximation method √(1+x) ≈ 1 + x/2, we get √1.04 = √(1+0.04) ≈ 1 + 0.02 = 1.02. The exact value is 1.019803902...
Method 1 (approximation): √1.04 = √(1+0.04) ≈ 1 + 0.04/2 = 1.02. Method 2 (fraction): 1.04 = 26/25, so √1.04 = √26/5 ≈ 5.099/5 = 1.0198.
Yes. √1.04 > 1 because 1.04 > 1. The square root of any number greater than 1 is also greater than 1. √1.04 ≈ 1.0198.
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