Square Root of 23

The square root of 23 is a number, which when multiplied by itself results in the original number 23. The square root of 23 is an irrational number since the value of square root 23 cannot be expressed in the form of p/q. In this article, we will learn the square root of 23 in decimal form, radical form and the procedure to find the value of square root 23 using the long division method with complete explanation.

Table of Contents:

• What Is The Square Root Of 23?
• Square Root Of 23 In Radical Form
• Square Root Of 23 By Long Division Method
• Examples
• FAQs

What is the Square Root of 23?

If a number is multiplied by itself and gives the result as 23, then the number is the square root 23. The square root of 23 is symbolically expressed as √23.

Hence, √23 = √(Number × Number)

Thus, if we multiply the number 4.7958 two times, we get the original value 23.

(i.e) √23 = √(4.7958× 4.7958)

√23 = √(4.7958)²

Now, remove square and square root, we get

√23 = ± 4.7958 (or)

√23 = ± 4.796 (Rounded to three decimal places)

Square Root of 23 in Radical Form

We can also represent the square root of 23 in the radical form. To express the square root of 23 in radical form, write the prime factorization of 23. The prime factorization of 23 is 23 So if we want to write √23 in radical form, it should be like √23. Hence, the simplest radical form of the square root of 23 is √23.

Square Root of 23 by Long Division Method

The procedure to find the square root of 23 using the long division method is given as follows:

Step 1: Write the number 23 in decimal form. To find the exact value of the square root of 23, add 6 zeros after the decimal point. Hence, 23 in decimal form is 23.000000. Now, pair the number 23 from right to left by putting the bar on the top of the number.

Step 2: Now, divide the number 23 by a number, such that the product of the same number should be less than or equal to 23. Thus, 4×4 =16, which is less than 23. Thus, we obtained the quotient = 4 and remainder = 7.

Step 3: Double the quotient value, so we get 8, and assume that 80 is the new divisor. Now, bring down the value 00 for division operation. So, the new dividend obtained is 700. Now, find the number, such that (80 + new number) × new number should give the product value, that should be less than or equal to 700. Hence, (80+7) × 7 = 609, which is less than 700.

Step 4: Now subtract 609 from 700, and we get 91 as the new reminder, and 47 as a quotient.

Step 5: The new quotient obtained is 47, and double that. Hence, we get 94 and assume that 940 is our new divisor. Now, bring down the two zeros and, we have 9100 as the new dividend.

Step 6: Find the number, such that (940 + new number) × new number should give the product value, that should be less than or equal to 9100. Thus, (940+9)× 9 = 8541, which is less than 9100.

Step 7: Subtract 8541 from 9100, and we get 559 as the new reminder.

Step 8: Continue this process until we get the approximate value of the square root of 23 up to three decimal places. (Note: keep the decimal point in the quotient value after bringing down all the values in the dividend).

Step 9: Thus, the approximate value of the square root of 23, √23 is 4.7958.

Video Lessons on Square Roots

Visualising square roots

Finding Square roots

Examples

Example 1:

Simplify 2+√23.

Solution:

Given: 2 +√23.

We know that the square root of 23 is 4.7958.

Now, substitute the value in the expression, we get:

2 +√23 = 2+4.7958

2+√23 = 6.7958.

Therefore, 2+√23 is 6.7958.

Example 2:

Find the value of x, if 7x + √23 = 14

Solution:

Given equation: 7x + √23 = 14 …(1)

We know that √23 = 4.7958.

Now, substitute the value in equation (1),

7x + 4.7958 = 14

7x = 14 – 4.7958

7x = 9.2042

x = (9.2042)/7

x = 1.314885

Therefore, the value of x is 1.315 (rounded to three decimal places).