15 Square Root Of 2

In Mathematics, the foursquare root of fifteen is a number that when multiplied by itself yields the original number fifteen. Because it cannot be stated in the course of p/q, the square root of 15 is an irrational number. In this post, we'll go through two singled-out means for finding the square root of 15 in detail such every bit the long division method and the prime factorization method.

Table of Contents:

What is the Value of Square Root of 15?
Radical Form of Square Root of 15
Prime number Factorization Method for the Square Root of 15
Long Division Method to Find Foursquare Root of 15
Examples
FAQs

What is the Value of Foursquare Root of 15?

The square of fifteen is a number if information technology is multiplied by itself and gives the outcome as fifteen. The square root of 15 is symbolically expressed equally √xv.

Hence, √15 = √(Value × Value)

Equally a result, multiplying three.8729 twice yields the original value of 15.

It ways √15 = √(3.8729× three.8729)

√15 = √(three.8729)²

When we accept away the square and square root, we become

√15 = ± 3.8729.

Square Root of fifteen in Decimal Form: 3.8729.

Square Root of fifteen in Radical Grade

The radical version of the square root of 15 can also be used. Nosotros can write the simplest radical form of the foursquare root of 15 if we know the prime factorization of 15. Every bit a result, fifteen's prime number factorization is 3× five. If it is written in radical class, it is √3×√ five (which isn't the nearly basic radical form). As a effect, √15 is the radical form of the square root of 15.

Square Root of 15 in Radical Form: √15.

Foursquare Root of 15 by Prime Factorization Method

To use the prime factorization method to find the √15, kickoff write the prime factorization of xv. Thus, the prime factorization of 15 is 3 × 5.

Thus, √15 = (√3). (√5)

We know that,

√three = 1.73205

√five = ii. 23606

Substitute the values of √ii and √5 in the equation above, we get

√15 = 1.732 × 2.236

√15 =3.8729 (approximately)

Square Root of 15 by Long Division Method

The post-obit is the approach for finding the √15 using the long division method:

Step 1: First, write the number 15 in decimal class. Add six zeros after the decimal point to become the verbal value of the √15. Equally a result, 15 is xv.000000 in decimal form. Now, past placing the bar on top of the number 15, couple it from right to left.

Step 2: Adjacent, split up fifteen by a number such that the product of the two same numbers is less than or equal to fifteen. Equally a result, three×3=nine, a number less than xv. As a result, nosotros have a quotient of 3 and a balance of 6.

Step 3: Multiply the quotient value by two, and we get six. Now, use 60 as the new divisor. Bring down the value 00 for the division operation. Every bit a event, the new dividend is 600. Find a number so that (60 + new number) × new number equals the production value, which must be less than or equal to 600. As a outcome, (sixty+8) × viii = 544, which is lower than 600.

Footstep iv: Subtracting 544 from 600 yields 56 equally the new reminder and 38 every bit the quotient.

Pace 5: Take the new caliber 38 and multiply it by two. Equally a effect, we become 76 and infer that our new divisor is 760. Again bringing downwardly two zeros, we now get a new dividend of 5600.

Step half dozen: Decide a number so that (760 + new number)× new number equals the product value, which must be less than or equal to 5600. As a effect, (760+7)× vii = 5369, a number smaller than 5600.

Pace 7: Subtract 5369 from 5600, and the new remainder is 231

Step 8: Repeat the steps until the estimated value of the √15 is obtained to three decimal places. (Afterward bringing down all the values in the dividend, keep the decimal point in the quotient value.)

Step 9: As a result, the square root of 15 is approximately iii.8729.

Square Root of 15

Video Lessons on Square Roots

Visualising foursquare roots

Finding Foursquare roots

Examples

Instance 1:

Reduce the expression: 12 +√15.

Solution:

Given: 12 +√xv.

We know that the √15 is iii.8729

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

12 +√15 = 12 + 3.8729

12 +√15 = 15.8729

Therefore, 12 +√fifteen is xv.8729.

Instance 2:

Simplify the expression: 3√15× iv√15.

Solution:

Given: three√15× 4√fifteen

three√15× 4√15 = (3×iv)(√15)²

three√xv× iv√15 = 12×15 = 180

Hence, the simplified form of three√15× 4√15 is180.

Example 3:

Calculate the value of k, if 2k+ √15 = 42.

Solution:

Given equation: 2k+ √15 = 42…(1)

Nosotros know that √15 = 3.8729.

Substitute the value in equation (one), we get

2k+3.8729 = 42

2k = 42 – 3.8729

2k = 38.1271

thou = (38.1271)/2

yard = 19.06355

Therefore, the value of k is 19.06, which is rounded to two decimal places.

Frequently Asked Questions on Foursquare Root of 15

What does the square root of xv equal?

The square root of 15 is approximately equivalent to 3.8729.

What is the foursquare root of 15 in radical form?

In radical course, the square root of 15 is √15.

Is √15 a rational number?

No, the square root of fifteen is not a rational number, as information technology cannot be expressed in the form of p/q.

What is the value of seven plus √15?

We know that √15 = iii.8729.
Hence, 7+√xv = vii+3.8729 = ten.8729.

What is the value of the foursquare of square root of 15?

The foursquare of square root of 15 is 15.

(i.e) (√15)² = 15.