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Square Root of 155

The square root of 155 is expressed as √155 in the radical form and as (155)^½ or (155)^0.5 in the exponent form. The square root of 155 rounded up to 8 decimal places is 12.44989960. It is the positive solution of the equation x² = 155.

Square Root of 155: 12.449899597988733
Square Root of 155 in exponential form: (155)^½ or (155)^0.5
Square Root of 155 in radical form: √155

Square Root of 155

1.	What is the Square Root of 155?
2.	How to find the Square Root of 155?
3.	Is the Square Root of 155 Irrational?
4.	FAQs

What is the Square Root of 155?

The square root of 155, (or root 155), is the number which when multiplied by itself gives the product as 155. Therefore, the square root of 155 = √155 = 12.449899597988733.

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How to Find Square Root of 155?

Square Root of 155 by Long Division Method

Value of √155 by Long Division Method

Explanation:

Forming pairs: 01 and 55
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 55, to the right of the remainder 0. The new dividend is now 55.
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 <= 55. After finding Z, together 2 and Z (2) form a new divisor 22 for the new dividend 55.
Divide 55 by 22 with the quotient as 2, giving the remainder = 55 - 22 × 2 = 55 - 44 = 11.
Now, let's find the decimal places after the quotient 12.
Bring down 00 to the right of this remainder 11. The new dividend is now 1100.
Add the last digit of quotient to divisor i.e. 2 + 22 = 24. To the right of 24, find a digit Z (which is 4) such that 24Z × Z <= 1100. Together they form a new divisor (244) for the new dividend (1100).
Divide 1100 by 244 with the quotient as 4, giving the remainder = 1100 - 244 × 4 = 1100 - 976 = 124.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 155.

Therefore, the square root of 155 by long division method is 12.4 approximately.

Is Square Root of 155 Irrational?

The actual value of √155 is undetermined. The value of √155 up to 25 decimal places is 12.44989959798873237483597. Hence, the square root of 155 is an irrational number.

☛ Also Check:

Square Root of 52 - √52 = 7.21110
Square Root of 12 - √12 = 3.46410
Square Root of 99 - √99 = 9.94987
Square Root of 136 - √136 = 11.66190
Square Root of 76 - √76 = 8.71780
Square Root of 841 - √841 = 29
Square Root of 140 - √140 = 11.83216

Square Root of 155 Solved Examples

Example 1: Solve the equation x² − 155 = 0

Solution:

x² - 155 = 0 i.e. x² = 155
x = ±√155
Since the value of the square root of 155 is 12.450,
⇒ x = +√155 or -√155 = 12.450 or -12.450.
Example 2: If the area of an equilateral triangle is 155√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 = 155√3 in²
⇒ a = ±√620 in
Since length can't be negative,
⇒ a = √620 = 2 √155
We know that the square root of 155 is 12.450.
⇒ a = 24.900 in
Example 3: If the surface area of a cube is 930 in². Find the length of the side of the cube.

Solution:

Let 'a' be the length of the side of the cube.
⇒ Area of the cube = 6a² = 930 in²
⇒ a = ±√155 in
Since length can't be negative,
⇒ a = √155
We know that the square root of 155 is 12.450.
⇒ a = 12.450 in

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FAQs on the Square Root of 155

What is the Value of the Square Root of 155?

The square root of 155 is 12.44989.

Why is the Square Root of 155 an Irrational Number?

Upon prime factorizing 155 i.e. 5¹ × 31¹, 5 is in odd power. Therefore, the square root of 155 is irrational.

Evaluate 5 plus 13 square root 155

The given expression is 5 + 13 √155. We know that the square root of 155 is 12.450. Therefore, 5 + 13 √155 = 5 + 13 × 12.450 = 5 + 161.849 = 166.849

What is the Square Root of 155 in Simplest Radical Form?

We need to express 155 as the product of its prime factors i.e. 155 = 5 × 31. Therefore, as visible, the radical form of the square root of 155 cannot be simplified further. Therefore, the simplest radical form of the square root of 155 can be written as √155

Is the number 155 a Perfect Square?

The prime factorization of 155 = 5¹ × 31¹. Here, the prime factor 5 is not in the pair. Therefore, 155 is not a perfect square.

What is the Square of the Square Root of 155?

The square of the square root of 155 is the number 155 itself i.e. (√155)² = (155)^2/2 = 155.

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