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Square Root of 159

The square root of 159 is expressed as √159 in the radical form and as (159)^½ or (159)^0.5 in the exponent form. The square root of 159 rounded up to 8 decimal places is 12.60952021. It is the positive solution of the equation x² = 159.

Square Root of 159: 12.609520212918492
Square Root of 159 in exponential form: (159)^½ or (159)^0.5
Square Root of 159 in radical form: √159

Square Root of 159

1.	What is the Square Root of 159?
2.	How to find the Square Root of 159?
3.	Is the Square Root of 159 Irrational?
4.	FAQs

What is the Square Root of 159?

The square root of 159, (or root 159), is the number which when multiplied by itself gives the product as 159. Therefore, the square root of 159 = √159 = 12.609520212918492.

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How to Find Square Root of 159?

Square Root of 159 by Long Division Method

Value of √159 by Long Division Method

Explanation:

Forming pairs: 01 and 59
Find a number Y (1) such that whose square is <= 1. Now divide 01 by 1 with quotient as 1.
Bring down the next pair 59, to the right of the remainder 0. The new dividend is now 59.
Add the last digit of the quotient (1) to the divisor (1) i.e. 1 + 1 = 2. To the right of 2, find a digit Z (which is 2) such that 2Z × Z <= 59. After finding Z, together 2 and Z (2) form a new divisor 22 for the new dividend 59.
Divide 59 by 22 with the quotient as 2, giving the remainder = 59 - 22 × 2 = 59 - 44 = 15.
Now, let's find the decimal places after the quotient 12.
Bring down 00 to the right of this remainder 15. The new dividend is now 1500.
Add the last digit of quotient to divisor i.e. 2 + 22 = 24. To the right of 24, find a digit Z (which is 6) such that 24Z × Z <= 1500. Together they form a new divisor (246) for the new dividend (1500).
Divide 1500 by 246 with the quotient as 6, giving the remainder = 1500 - 246 × 6 = 1500 - 1476 = 24.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 159.

Therefore, the square root of 159 by long division method is 12.6 approx.

Is Square Root of 159 Irrational?

The actual value of √159 is undetermined. The value of √159 up to 25 decimal places is 12.60952021291849153122863. Hence, the square root of 159 is an irrational number.

☛ Also Check:

Square Root of 75 - √75 = 8.66025
Square Root of 26 - √26 = 5.09902
Square Root of 2 - √2 = 1.41421
Square Root of 361 - √361 = 19
Square Root of 68 - √68 = 8.24621
Square Root of 74 - √74 = 8.60233
Square Root of 116 - √116 = 10.77033

Square Root of 159 Solved Examples

Example 1: Solve the equation x² − 159 = 0

Solution:

x² - 159 = 0 i.e. x² = 159
x = ±√159
Since the value of the square root of 159 is 12.610,
⇒ x = +√159 or -√159 = 12.610 or -12.610.
Example 2: If the area of a circle is 159π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 159π in²
⇒ r = ±√159 in
Since radius can't be negative,
⇒ r = √159
The square root of 159 is 12.610.
⇒ r = 12.610 in
Example 3: If the surface area of a sphere is 636π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 636π in²
⇒ r = ±√159 in
Since radius can't be negative,
⇒ r = √159
The square root of 159 is 12.610.
⇒ r = 12.610 in

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FAQs on the Square Root of 159

What is the Value of the Square Root of 159?

The square root of 159 is 12.60952.

Why is the Square Root of 159 an Irrational Number?

Upon prime factorizing 159 i.e. 3¹ × 53¹, 3 is in odd power. Therefore, the square root of 159 is irrational.

What is the Square Root of 159 in Simplest Radical Form?

We need to express 159 as the product of its prime factors i.e. 159 = 3 × 53. Therefore, as visible, the radical form of the square root of 159 cannot be simplified further. Therefore, the simplest radical form of the square root of 159 can be written as √159

What is the Value of 15 square root 159?

The square root of 159 is 12.610. Therefore, 15 √159 = 15 × 12.610 = 189.143.

What is the Square of the Square Root of 159?

The square of the square root of 159 is the number 159 itself i.e. (√159)² = (159)^2/2 = 159.

If the Square Root of 159 is 12.610. Find the Value of the Square Root of 1.59.

Let us represent √1.59 in p/q form i.e. √(159/100) = 1.59/10 = 1.261. Hence, the value of √1.59 = 1.261

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