Square Root of 42

The square root of 42 is a number, which when multiplied by itself results in the original number 42. The square root of 42 is an irrational number since the value of square root 42 cannot be expressed in the form of p/q. The square root of 42 can be found using two different methods, such as long division and prime factorization methods. In this article, we are going to learn the square root of 42 in decimal form, radical form and the procedure to find the value of square root 42 using the two different methods with complete explanation.

Table of Contents:

• What Is The Square Root Of 42?
• Square Root Of 42 In Radical Form
• Square Root Of 42 By Prime Factorization Method
• Square Root Of 42 By Long Division Method
• Examples
• FAQs

What is the Square Root of 42?

If a number is multiplied by itself and gives the result as 42, then the number is the square root 42. The square root of 42 is symbolically expressed as √42.

Hence, √42 = √(Number × Number)

Thus, if we multiply the number 6.4807 two times, we get the original value 42.

(i.e) √42 = √(6.4807× 6.4807)

√42 = √(6.4807)²

Now, remove square and square root, we get

√42 = ± 6.4807 (or)

√42 = ± 6.481 (Rounded to three decimal places)

Square Root of 42 in Radical Form

We can also represent the square root of 42 in the radical form. To express the square root of 42 in radical form, write the prime factors of 42. The number 42 has three prime factors, such as 2, 3 and 7. So, if we want to write √42 in radical form, it should be like √2. √3. √7, which is not in the simplest form. So, we can say the square root of 42 is radical form is √42

Square Root of 42 by Prime Factorization Method

To find the square root of 42 using the prime factorization method, we need to know the prime factors of 42. The prime factors of 42 are 2, 3 and 7 and the prime factorization of 42 is 2× 3×7.

Thus, √42 = √2. √3.√7

We know that,

√2 = 1.414

√3 = 1.732

√7 = 2.646

Now, substitute the values of √2, √3 and √7 in the above equation.

√42 = 1.414 × 1.732 × 2.646

√42 = 6.481 (approximately)

Hence, the square root of 42 in decimal form is approximately equal to 6.481 (rounded to three decimal places)

Square Root of 42 by Long Division Method

The procedure to find the square root of 42 using the long division method is given as follows:

Step 1: Write the number 42 in decimal form. To find the exact value of the square root of 42, add 6 zeros after the decimal point. Hence, 42 in decimal form is 42.000000. Now, pair the number 42 from right to left by putting the bar on the top of the number.

Step 2: Now, divide the number 42 by a number, such that the product of the same number should be less than or equal to 42. Thus, 6×6 =36, which is less than 42. Thus, we obtained the quotient = 6 and remainder = 6.

Step 3: Double the quotient value, so we get 12, and assume that 120 is the new divisor. Now, bring down the value 00 for division operation. So, the new dividend obtained is 600. Now, find the number, such that (120 + new number) × new number should give the product value, that should be less than or equal to 600. Hence, (120+4) × 4 = 496, which is less than 600.

Step 4: Now subtract 496 from 600, and we get 104 as the new reminder, and 64 as a quotient.

Step 5: The new quotient obtained is 64, and double that. Hence, we get 128 and assume that 1280 is our new divisor. Now, bring down the two zeros and, we have 10400 as the new dividend.

Step 6: Find the number, such that (1280 + new number) × new number should give the product value, that should be less than or equal to 10400. Thus, (1280+8)× 8 = 10304, which is less than 10400.

Step 7: Subtract 10304 from 10400, and we get 96 as the new reminder.

Step 8: Continue this process until we get the approximate value of the square root of 42 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 42, √42 is 6.4807.

Video Lessons on Square Roots

Visualising square roots

Finding Square roots

Examples

Example 1:

Simplify 4+√42.

Solution:

Given: 4+√42.

We know that the square root of 42 is 6.481.

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

4+√42 = 4+6.481

4+√42 = 10.481.

Therefore, 4+√42 is 10.481.

Example 2:

Find the value of x, if 5x + √42 = 10

Solution:

Given equation: 5x + √42 = 10 …(1)

We know that √42 = 6.481.

Now, substitute the value in equation (1),

5x + 6.481 = 10

5x = 10 – 6.481

5x = 3.519

x = (3.519)/5

x = 0.7038

Therefore, the value of x is 0.704 (rounded to three decimal places).