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Square Root of 157

The square root of 157 is expressed as √157 in the radical form and as (157)^½ or (157)^0.5 in the exponent form. The square root of 157 rounded up to 9 decimal places is 12.529964086. It is the positive solution of the equation x² = 157.

Square Root of 157: 12.529964086141668
Square Root of 157 in exponential form: (157)^½ or (157)^0.5
Square Root of 157 in radical form: √157

Square Root of 157

1.	What is the Square Root of 157?
2.	How to find the Square Root of 157?
3.	Is the Square Root of 157 Irrational?
4.	FAQs

What is the Square Root of 157?

The square root of 157, (or root 157), is the number which when multiplied by itself gives the product as 157. Therefore, the square root of 157 = √157 = 12.529964086141668.

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How to Find Square Root of 157?

Square Root of 157 by Long Division Method

Value of √157 by Long Division Method

Explanation:

Forming pairs: 01 and 57
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 57, to the right of the remainder 0. The new dividend is now 57.
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 <= 57. After finding Z, together 2 and Z (2) form a new divisor 22 for the new dividend 57.
Divide 57 by 22 with the quotient as 2, giving the remainder = 57 - 22 × 2 = 57 - 44 = 13.
Now, let's find the decimal places after the quotient 12.
Bring down 00 to the right of this remainder 13. The new dividend is now 1300.
Add the last digit of quotient to divisor i.e. 2 + 22 = 24. To the right of 24, find a digit Z (which is 5) such that 24Z × Z <= 1300. Together they form a new divisor (245) for the new dividend (1300).
Divide 1300 by 245 with the quotient as 5, giving the remainder = 1300 - 245 × 5 = 1300 - 1225 = 75.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 157.

Therefore, the square root of 157 by long division method is 12.5 approx.

Is Square Root of 157 Irrational?

The actual value of √157 is undetermined. The value of √157 up to 25 decimal places is 12.52996408614166778849536. Hence, the square root of 157 is an irrational number.

☛ Also Check:

Square Root of 41 - √41 = 6.40312
Square Root of 36 - √36 = 6
Square Root of 256 - √256 = 16
Square Root of 13 - √13 = 3.60555
Square Root of 116 - √116 = 10.77033
Square Root of 1681 - √1681 = 41
Square Root of 120 - √120 = 10.95445

Square Root of 157 Solved Examples

Example 1: Solve the equation x² − 157 = 0

Solution:

x² - 157 = 0 i.e. x² = 157
x = ±√157
Since the value of the square root of 157 is 12.530,
⇒ x = +√157 or -√157 = 12.530 or -12.530.
Example 2: If the surface area of a sphere is 628π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 628π in²
⇒ r = ±√157 in
Since radius can't be negative,
⇒ r = √157
The square root of 157 is 12.530.
⇒ r = 12.530 in
Example 3: If the area of an equilateral triangle is 157√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 = 157√3 in²
⇒ a = ±√628 in
Since length can't be negative,
⇒ a = √628 = 2 √157
We know that the square root of 157 is 12.530.
⇒ a = 25.060 in

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FAQs on the Square Root of 157

What is the Value of the Square Root of 157?

The square root of 157 is 12.52996.

Why is the Square Root of 157 an Irrational Number?

The number 157 is prime. This implies that the number 157 is pairless and is not in the power of 2. Therefore, the square root of 157 is irrational.

Is the number 157 a Perfect Square?

The number 157 is prime. This implies that the square root of 157 cannot be expressed as a product of two equal integers. Therefore, the number 157 is not a perfect square.

If the Square Root of 157 is 12.530. Find the Value of the Square Root of 1.57.

Let us represent √1.57 in p/q form i.e. √(157/100) = 1.57/10 = 1.253. Hence, the value of √1.57 = 1.253

What is the Value of 7 square root 157?

The square root of 157 is 12.530. Therefore, 7 √157 = 7 × 12.530 = 87.710.

What is the Square Root of 157 in Simplest Radical Form?

The number 157 is a prime number. This implies that the number 157 is pairless and is not in the power of 2. Therefore, the radical form of square root of 157 cannot be simplified further.

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