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Determine Rational or Irrational Numbers (Square Roots and Decimals Only)
Determine Rational or Irrational Numbers (Square Roots and Decimals Only)

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Square Root 1 to 25

Square root 1 to 25 is the list of square roots of all the numbers from 1 to 25. Square root can have both negative and positive values. The positive values of square roots from 1 to 25 range from 1 to 5.

In square roots 1 to 25, the numbers 1, 4, 9, 16, and 25 are perfect squares and the remaining numbers are non-perfect squares i.e. their square root will be irrational. The square root 1 to 25 in radical form is expressed as √x and in the exponential form, it is expressed as (x)½.

Square Roots 1 to 25:

  • In radical form: √x
  • In exponential form: (x)½

Where x is any number between 1 to 25.

1. Square Root from 1 to 25
2. Square Root 1 to 25 PDF
3. How to Calculate Square Root 1 to 25?
4. FAQs

Square Root from 1 to 25 Chart

Square Root from 1 to 25

Learning square root 1 to 25 will help you to simplify the time-consuming long equations quickly. The value of square roots 1 to 25 up to 3 decimal places is listed in the table below.

Square Root from 1 to 25 Rounded to 3 Decimal Places

√1 = 1

√2 = 1.414

√3 = 1.732

√4 = 2

√5 = 2.236

√6 = 2.449

√7 = 2.646

√8 = 2.828

√9 = 3

√10 = 3.162

√11 = 3.317

√12 = 3.464

√13 = 3.606

√14 = 3.742

√15 = 3.873

√16 = 4

√17 = 4.123

√18 = 4.243

√19 = 4.359

√20 = 4.472

√21 = 4.583

√22 = 4.690

√23 = 4.796

√24 = 4.899

√25 = 5

The students are advised to memorize these square roots 1 to 25 values thoroughly for faster math calculations. Click on the download button to save its PDF copy.

Square Root 1 to 25 for Perfect Squares

The table below shows the values of square roots from 1 to 25 for perfect squares.

√1 = 1

√4 = 2

√9 = 3

√16 = 4

√25 = 5

Square Root 1 to 25 for Non-Perfect Squares

The table below shows the values of 1 to 25 square roots for non-perfect squares.

√2 = 1.414

√3 = 1.732

√5 = 2.236

√6 = 2.449

√7 = 2.646

√8 = 2.828

√10 = 3.162

√11 = 3.317

√12 = 3.464

√13 = 3.606

√14 = 3.742

√15 = 3.873

√17 = 4.123

√18 = 4.243

√19 = 4.359

√20 = 4.472

√21 = 4.583

√22 = 4.690

√23 = 4.796

√24 = 4.899

☛ Check: Square Root Calculator

How to Calculate Square Root from 1 to 25?

Method 1: Prime Factorization

Example: Value of √25

  • Prime factorization of 25 is 5 × 5
  • Pairing prime factors: 5

Therefore, the value of √25 = 5

Method 2: Long Division Method

Square Roots of Numbers Between 1 to 25

Solved Examples on Square Root 1 to 25

  1. Example 1: A square metal sheet has an area of 18 sq. inches. Find the length of the side of the metal sheet.

    Solution:

    Let ‘a’ be the length of the side of the metal sheet

    Area of the square metal sheet = 18 in2 = a2

    i.e. a2 = 18

    a = √18 = 4.243 in

    Therefore, the length of the side of the metal sheet is 4.243 inches.

  2. Example 2: If a circular tabletop has an area of 19π sq. inches. Find the radius of the tabletop in inches?

    Solution:

    Area of circular tabletop = 19π in2 = πr2

    i.e. 19 = r2. Hence, radius = √19

    Using the values from 1 to 25 square root chart, the radius of the tabletop = 4.359 inches.

  3. Example 3: Find the value of 6√7 + 3√7.

    Solution:

    6√7 + 3√7 = 6 × (2.646) + 3 × (2.646) = 9 × 2.646 [the value of √7 = 2.646]

    Therefore, 6√7 + 3√7 = 9 × 2.646 = 23.814

FAQs on Square Root 1 to 25

What is the Value of Square Root 1 to 25?

The value of square root 1 to 25 is a number (x1/2) when multiplied by itself gives the original number. It can have both negative and positive values. Between 1 to 25, the square roots of 1, 4, 9, 16, and 25 are whole numbers (rational), while the square roots of 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, and 24 are decimal numbers that are neither terminating nor recurring (irrational).

What are the Methods to Calculate Square Roots from 1 to 25?

There are two methods commonly used to calculate the value of square roots from 1 to 25. For perfect squares (1, 4, 9, 16, and 25), we can use prime factorization method and for non-perfect squares (2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, and 24) long division method can be used.

What Values of Square Roots from 1 to 25 are Between 2 and 3 inclusive?

The values of square roots 1 to 25 between 2 and 3 are √4 (2), √5 (2.236), √6 (2.449), √7 (2.646), √8 (2.828), and √9 (3).

What is the Value of 10 Plus 2 Square Root 25?

The value of √25 is 5. So, 10 + 2 × √25 = 10 + 2 × 5 = 20. Hence, the value of 10 plus 2 square root 25 is 20.

How Many Numbers in Square Roots 1 to 25 are Rational?

The numbers 1, 4, 9, 16, and 25 are perfect squares so their square roots will be whole numbers i.e. can be expressed in the form of p/q where q ≠ 0. Hence, the square root of the numbers 1, 4, 9, 16, and 25 are rational numbers.

If you take Square Root from 1 to 25, how many of them will be Irrational?

The numbers 2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, and 24 are non-perfect squares. Hence their square root will be an irrational number (cannot be expressed in the form of p/q where q ≠ 0).

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