A day full of math games & activities. Find one near you.

Square Root of 151

The square root of 151 is expressed as √151 in the radical form and as (151)^½ or (151)^0.5 in the exponent form. The square root of 151 rounded up to 8 decimal places is 12.28820573. It is the positive solution of the equation x² = 151.

Square Root of 151: 12.288205727444508
Square Root of 151 in exponential form: (151)^½ or (151)^0.5
Square Root of 151 in radical form: √151

Square Root of 151

1.	What is the Square Root of 151?
2.	How to find the Square Root of 151?
3.	Is the Square Root of 151 Irrational?
4.	FAQs

What is the Square Root of 151?

The square root of 151, (or root 151), is the number which when multiplied by itself gives the product as 151. Therefore, the square root of 151 = √151 = 12.288205727444508.

☛ Check: Square Root Calculator

How to Find Square Root of 151?

Square Root of 151 by Long Division Method

Value of √151 by Long Division Method

Explanation:

Forming pairs: 01 and 51
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 51, to the right of the remainder 0. The new dividend is now 51.
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 <= 51. After finding Z, together 2 and Z (2) form a new divisor 22 for the new dividend 51.
Divide 51 by 22 with the quotient as 2, giving the remainder = 51 - 22 × 2 = 51 - 44 = 7.
Now, let's find the decimal places after the quotient 12.
Bring down 00 to the right of this remainder 7. The new dividend is now 700.
Add the last digit of quotient to divisor i.e. 2 + 22 = 24. To the right of 24, find a digit Z (which is 2) such that 24Z × Z <= 700. Together they form a new divisor (242) for the new dividend (700).
Divide 700 by 242 with the quotient as 2, giving the remainder = 700 - 242 × 2 = 700 - 484 = 216.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 151.

Therefore, the square root of 151 by long division method is 12.2 approximately.

Is Square Root of 151 Irrational?

The actual value of √151 is undetermined. The value of √151 up to 25 decimal places is 12.28820572744450759181216. Hence, the square root of 151 is an irrational number.

☛ Also Check:

Square Root of 65 - √65 = 8.06226
Square Root of 63 - √63 = 7.93725
Square Root of 841 - √841 = 29
Square Root of 30 - √30 = 5.47723
Square Root of 1000 - √1000 = 31.62278
Square Root of 14 - √14 = 3.74166
Square Root of 97 - √97 = 9.84886

Square Root of 151 Solved Examples

Example 1: Solve the equation x² − 151 = 0

Solution:

x² - 151 = 0 i.e. x² = 151
x = ±√151
Since the value of the square root of 151 is 12.288,
⇒ x = +√151 or -√151 = 12.288 or -12.288.
Example 2: If the area of an equilateral triangle is 151√3 in². Find the length of one of the sides of the triangle.

Solution:

Let 'a' be the length of one of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a² = 151√3 in²
⇒ a = ±√604 in
Since length can't be negative,
⇒ a = √604 = 2 √151
We know that the square root of 151 is 12.288.
⇒ a = 24.576 in
Example 3: If the area of a circle is 151π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 151π in²
⇒ r = ±√151 in
Since radius can't be negative,
⇒ r = √151
The square root of 151 is 12.288.
⇒ r = 12.288 in

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on the Square Root of 151

What is the Value of the Square Root of 151?

The square root of 151 is 12.2882.

Why is the Square Root of 151 an Irrational Number?

The number 151 is prime. This implies that the number 151 is pairless and is not in the power of 2. Therefore, the square root of 151 is irrational.

If the Square Root of 151 is 12.288. Find the Value of the Square Root of 1.51.

Let us represent √1.51 in p/q form i.e. √(151/100) = 1.51/10 = 1.229. Hence, the value of √1.51 = 1.229

Is the number 151 a Perfect Square?

The number 151 is prime. This implies that the square root of 151 cannot be expressed as a product of two equal integers. Therefore, the number 151 is not a perfect square.

Evaluate 14 plus 20 square root 151

The given expression is 14 + 20 √151. We know that the square root of 151 is 12.288. Therefore, 14 + 20 √151 = 14 + 20 × 12.288 = 14 + 245.764 = 259.764

What is the Square Root of -151?

The square root of -151 is an imaginary number. It can be written as √-151 = √-1 × √151 = i √151 = 12.288i
where i = √-1 and it is called the imaginary unit.

Math worksheets and
visual curriculum