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Square Root 1 to 10

Square root 1 to 10 is the list of square roots of all the numbers from 1 to 10. Square root can have both negative and positive values. The positive values of square roots from 1 to 10 range from 1 to 3.16228.

In square roots 1 to 10, the numbers 1, 4, and 9 are perfect squares and the remaining numbers are non-perfect squares i.e. their square root will be irrational. The square root 1 to 10 in radical form is expressed as √x and in the exponential form it is expressed as (x)½.

Square Roots 1 to 10:

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

Where x is any number between 1 to 10.

1. Square Root from 1 to 10
2. Square Root 1 to 10 PDF
3. How to Calculate Square Root 1 to 10?
4. FAQs

Square Root from 1 to 10 Chart

Square Root from 1 to 10

Learning square root 1 to 10 will help you to simplify the time-consuming long equations quickly. The value of square roots 1 to 10 up to 3 decimal places is listed in the table below.

Square Root from 1 to 10 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

The students are advised to memorize these square roots 1 to 10 values thoroughly for faster math calculations. Click on the download button to save its PDF copy.

Square Root 1 to 10 for Perfect Squares

The table below shows the values of square roots from 1 to 10 for perfect squares.

√1 = 1

√4 = 2

√9 = 3

Square Root 1 to 10 for Non-Perfect Squares

The table below shows the values of 1 to 10 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

☛ Check: Square Root Calculator

How to Calculate Square Root from 1 to 10?

Method 1: Prime Factorization

Example: Value of √9

  • Prime factorization of 9 is 3 × 3
  • Pairing prime factors: 3

Therefore, the value of √9 = 3

Method 2: Long Division Method

Example: Value of √3

Square Roots of Numbers Between 1 to 10

Solved Examples on Square Root 1 to 10

  1. Example 1: A square metal sheet has an area of 10 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 = 10 in2 = a2

    i.e. a2 = 10

    a = √10 = 3.162 in

    Therefore, the length of the side of the metal sheet is 3.162 inches.

  2. Example 2: If a circular tabletop has an area of 7π sq. inches. Find the radius of the tabletop in inches?

    Solution:

    Area of circular tabletop = 7π in2 = πr2

    i.e. 7 = r2. Hence, radius = √7

    Using the values from 1 to 10 square root chart, the radius of the tabletop = 2.646 inches.

  3. Example 3: Find the value of 17√4 + 12√9

    Solution:

    17√4 + 12√9 = 17 × (2) + 12 × (3) [the value of √4 = 2 and √9 = 3]

    Therefore, 17√4 + 12√9 = 34 + 36 = 70

FAQs on Square Root 1 to 10

What is the Value of Square Root 1 to 10?

The value of square root 1 to 10 is a number (x1/2) when multiplied by itself gives the original number. It can have both negative and positive values. Between 1 to 10, the square roots of 1, 4, and 9 are whole numbers (rational), while the square roots of 2, 3, 5, 6, 7, 8, and 10 are decimal numbers that are neither terminating nor recurring (irrational).

What is the Value of 21 Plus 2 Square Root 9?

The value of √9 is 3. So, 21 + 2 × √9 = 21 + 2 × 3 = 27. Hence, the value of 21 plus 2 square root 9 is 27.

What are the Methods to Calculate Square Roots from 1 to 10?

There are two methods commonly used to calculate the value of square roots from 1 to 10. For perfect squares (1, 4, and 9), we can use prime factorization method and for non-perfect squares (2, 3, 5, 6, 7, 8, and 10) long division method can be used.

If you Take Square Root from 1 to 10, how many of them will be Irrational?

The numbers 2, 3, 5, 6, 7, 8, and 10 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).

What Values of Square Roots from 1 to 10 are Between 1 and 3 inclusive?

The values of square roots 1 to 10 between 1 and 3 are √1 (1), √2(1.414), √3(1.732), √4 (2), √5 (2.236), √6 (2.449), √7 (2.646), √8 (2.828), and √9 (3).

How Many Numbers in Square Roots 1 to 10 are Rational?

The numbers 1, 4, and 9 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, and 9 are rational numbers.

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