Square Root of 30

The square root of 30 is a number, which when multiplied by itself resulting in the original number 30. The square root of 30 is an irrational number as the value of square root 30 cannot be expressed in the form of p/q. The two different methods to find the square root of 30 are the long division method and prime factorization method. In this article, we are going to learn the square root of 30 in decimal form, radical form and the procedure to find the value of square root 30 using the two different methods in a detailed way.

What is the Value of Square Root of 30?

If a number is multiplied by itself and gives the result as 30, then the number is the square root 30. The square root of 30 is symbolically expressed as √30.

Hence, √30 = √(Number × Number)

Thus, if we multiply the number 5.477 two times, we get the original value 30.

(i.e) √30 = √(5.477× 5.477)

√30 = √(5.477)²

Now, remove square and square root, we get

√30 = ± 5.477 (Rounded to three decimal places)

Square Root of 30 in Radical Form

The square root of 30 can also be expressed in the radical form. If we know the prime factorization of 30, we can write the simplest radical form of the square root of 30. Thus, the prime factorization of 30 is 2×3×5. If it is written in the radical form (i.e) √2×√3×√5, it should not be the simplest form. Hence, the simplest radical form of the square root of 30 is √30.

Square Root of 30 by Prime Factorization Method

To find the square root of 30 using the prime factorization method, we need to know the prime factors of 30. The prime factors of 30 are 2, 3 and 5 and the prime factorization of 30 is 2×3×5.

Thus, √30 = √2. √3.√5

We know that,

√2 = 1.414

√3 = 1.732

√5 = 2.236

Now, substitute the values of √2, √3 and √5 in the above equation.

√30 = 1.414 × 1.732 × 2.236

√30 = 5. 4772255 (approximately)

Hence, the square root of 30 in decimal form is 5.477 (rounded to three decimal places)

Square Root of 30 by Long Division Method

The procedure to find the square root of 30 using the long division method is given as follows:

Step 1: Write the number 30 in decimal form. To find the exact value of the square root of 30, add 6 zeros after the decimal point. Hence, 30 in decimal form is 30.000000. Now, pair the number 30 from right to left by putting the bar on the top of the number.

Step 2: Now, divide the number 30 by a number, such that the product of the same number should be less than or equal to 30. Thus, 5×5 =25, which is less than 30. Thus, we obtained the quotient = 5 and remainder = 5.

Step 3: Double the quotient value, so we get 10, and assume that 100 is the new divisor. Now, bring down the value 00 for division operation. So, the new dividend obtained is 500. Now, find the number, such that (100 + new number) × new number should give the product value, that should be less than or equal to 500. Hence, (100+4) × 4 = 416, which is less than 500.

Step 4: Now subtract 416 from 500, and we get 84 as the new reminder, and 54 as a quotient.

Step 5: The new quotient obtained is 54, and double that. Hence, we get 108 and assume that 1080 is our new divisor. Now, bring down the two zeros and, we have 8400 as the new dividend.

Step 6: Find the number, such that (1080 + new number) × new number should give the product value, that should be less than or equal to 8400. Thus, (1080+7)× 7 = 7609, which is less than 8400.

Step 7: Subtract 7609 from 8400, and we get 791 as the new reminder.

Step 8: Continue this process until we get the approximate value of the square root of 30 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 30, √30 is 5.477.

Video Lessons on Square Roots

Visualising square roots

Finding Square roots

Examples

Example 1:

Simplify 20√30.

Solution:

Given: 20√30.

We know that the square root of 30 is 5.477.

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

20√30 = 20(5.477)

20√30 = 109.54

Therefore, 20√30 is 109.54.

Example 2:

Find the value of m, if 10m+2√30 = 150

Solution:

Given equation: 10m+2√30 = 150…(1)

We know that √30 = 5.477.

Now, substitute the value in equation (1),

10m+2(5.477) = 150

10m + 10.954 = 150

10m = 150 – 10.954

10m = 139.046

m = 139.046/10

m = 13.9046

Therefore, the value of m is 13.9046.