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How to Obtain Square Root

Learn how to obtain square roots by factor pairs, estimation, calculators, and checking answers, with mistakes, troubleshooting, and FAQs.

EducationEdited by Pramod Tiwari
2 min read

Quick Answer

To obtain a square root, find the number that multiplies by itself to equal the original number. For perfect squares use known facts, and for non-perfect squares use estimation or a calculator.

What You Need

  • Number to evaluate
  • Multiplication facts
  • Calculator if needed
  • Paper for factor work
  • Rounding rule if using decimals

Safety Precautions

  • Check whether the question wants an exact or decimal answer.
  • Remember that positive numbers have positive and negative square roots in algebra contexts.
  • Do not round too early in multi-step problems.
  • Use the correct calculator button for square root, not square.

Step-by-Step Instructions

  1. Step 1

    Understand the meaning

    The square root of a number is a value that gives the number when multiplied by itself.

  2. Step 2

    Check perfect squares

    Compare the number to common squares such as 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.

  3. Step 3

    Use factors if possible

    Break the number into factors and look for square factors.

  4. Step 4

    Estimate between squares

    For non-perfect squares, locate the two perfect squares around it.

  5. Step 5

    Use a calculator

    Press the square root button for a decimal approximation.

  6. Step 6

    Round if required

    Round only to the place value requested by the problem.

  7. Step 7

    Check by squaring

    Multiply your answer by itself to see whether it returns the original number.

Practical Example

Example: The square root of 49 is 7 because 7 x 7 = 49. The square root of 50 is a little more than 7 because 50 is between 49 and 64.

Common Mistakes

  • Confusing square and square root
  • Forgetting negative roots in algebra
  • Rounding too early
  • Assuming every square root is a whole number
  • Typing the wrong calculator operation
  • Not checking the answer by squaring

Troubleshooting

The result is a long decimal

The number is probably not a perfect square; round according to the assignment.

Calculator gives an error

You may be trying to take the square root of a negative number in a real-number setting.

Answer seems too large

Square it to check. A square root should usually be smaller than the original number when the number is greater than 1.

Exact form is required

Simplify using square factors instead of converting to a decimal.

FAQs

What is the square root of 64?

The principal square root of 64 is 8.

Can square roots be negative?

The principal square root is nonnegative, but equations like x squared equals 9 have two solutions: 3 and -3.

What is a perfect square?

A perfect square is a number made by multiplying a whole number by itself.

How do I check a square root?

Square your answer and compare it with the original number.

Education2 min read

How to Learn Math

Learn how to learn math with foundations, examples, practice, mistake review, problem-solving habits, troubleshooting, and FAQs.

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