Square Root of 1250: How to Find the Square root of 1250

Finding the square root of 1250 is a great way to improve your arithmetic skills. This article makes it easy to figure out how to apply long division to find the decimal value or prime factorisation to find the exact radical form.

How To Find Square Root of 1250?

The integer that, when multiplied by itself, generates 1250 is the square root of 1250.

• Decimal Value: \approx 35.355

• Radical Form (Simplest): 25\sqrt{2}

• Exponential Form: (1250)^{1/2} or (1250)^{0.5}

Is 1250 a square number? No. A number like 25 (5 \times 5) or 100 (10 \times 10) is a perfect square. We receive a decimal response since no whole number times itself equals 1250.

Square Root of 1250 to More Decimal Places

[

\sqrt{1250} = 25\sqrt{2} \approx 35.3553390593\ldots

]

Rounded values:

 3 decimal places: 35.355

 5 decimal places: 35.35534

 10 decimal places: 35.3553390593

Read More - Perfect Squares – Definition and Methods

Steps to Find Square Root of 1250

The Prime Factorisation Method and the Long Division Method are the two best approaches to find the square root of 1250.

1. Prime Factorization Method (For Radical Form)

This method helps us identify the "simplest form" of the square root.

How to find the square root of 1250:

1. Factor 1250 into prime numbers: 1250 = 2 \times 625
   625 = 5 \times 125
   125 = 5 \times 25
   25 = 5 \times 5
   So, 1250 = 2 \times 5 \times 5 \times 5 \times 5 = 2 \times 5^4

2. Group the factors into pairs:
   1250 = (5 \times 5) \times (5 \times 5) \times 2

3. Take one number from each pair out of the root:
   \sqrt{1250} = 5 \times 5 \times \sqrt{2}
   \sqrt{1250} = 25\sqrt{2}

2. Long Division Method (For Decimal Value)

If you need to find the precise decimal digits, use this method.

• Step 1:  Put the numbers into pairs from right to left: 12 and 50.

• Step 2: Find the biggest number whose square is less than or equal to 12. That is three (3 times 3 is 9).

• Step 3: Take 9 away from 12 (Remainder = 3) and bring down the next two numbers (50). Your new number is 350.

• Step 4: Multiply your answer by 2 (3 \times 2 = 6). Find a number x that goes next to 6 (6x \times x) that is less than or equal to 350.
  If we pick 5: 65 \times 5 = 325.

• Step 5: Subtract 325 from 350. Remainder is 25.

• Step 6: Add two zeros and a decimal point. Keep going! 

The result is 35.355...

Read More - Basic Math Formulas Chart for Quick Study

Quick Reference Table

This is a quick reference table that can help you comprehend the square root of 1250:

Square Root of 1250 Solved Examples

The square root of 1250 appears in algebra, geometry, and quick estimation questions. Since (1250) is not a perfect square, its square root is written in exact form as (25\sqrt{2}) and in decimal form as approximately (35.355). The solved examples below show how to use this value in different question types students commonly see in homework and exams.

 1) Solved Equation Example

Question: Solve (x^2 - 1250 = 0)

Solution:

 (x^2 - 1250 = 0)

 (x^2 = 1250)

 (x = \pm \sqrt{1250})

 (x = \pm 25\sqrt{2})

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Using decimal form:

 (x \approx \pm 35.355)

Answer: (x = 25\sqrt{2}) or (x = -25\sqrt{2})

 2) Radius of a Sphere from Surface Area

Question: The surface area of a sphere is (5000\pi) square units. Find its radius.

Solution:

 Surface area of sphere (= 4\pi r^2)

 (4\pi r^2 = 5000\pi)

 (4r^2 = 5000)

 (r^2 = 1250)

 (r = \sqrt{1250} = 25\sqrt{2})

Radius is always positive.

Answer: (r = 25\sqrt{2}) units (\approx 35.355) units

 3) Side of a Cube from Surface Area

Question: The total surface area of a cube is (7500) square units. Find the side length.

Solution:

 Surface area of cube (= 6a^2)

 (6a^2 = 7500)

 (a^2 = 1250)

 (a = \sqrt{1250} = 25\sqrt{2})

Side length cannot be negative.

Answer: (a = 25\sqrt{2}) units (\approx 35.355) units

 4) Rectangle Diagonal Example

Question: A rectangle has length (25) units and breadth (25) units. Find the diagonal.

Solution:

Using Pythagoras theorem:

 (d = \sqrt{25^2 + 25^2})

 (d = \sqrt{625 + 625})

 (d = \sqrt{1250})

 (d = 25\sqrt{2})

Answer: Diagonal (= 25\sqrt{2}) units (\approx 35.355) units

 5) Simplification and Verification Example

Question: Simplify (\sqrt{1250}) and verify by squaring the result.

Solution:

 (1250 = 2 \times 5^4)

 (\sqrt{1250} = \sqrt{2 \times 5^4})

 (\sqrt{1250} = 5^2\sqrt{2} = 25\sqrt{2})

Verification:

 ((25\sqrt{2})^2 = 25^2 \times 2)

 (= 625 \times 2 = 1250)

Answer: (\sqrt{1250} = 25\sqrt{2})

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