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Square Root of 154

The square root of 154 is expressed as √154 in the radical form and as (154)^½ or (154)^0.5 in the exponent form. The square root of 154 rounded up to 5 decimal places is 12.40967. It is the positive solution of the equation x² = 154.

Square Root of 154: 12.409673645990857
Square Root of 154 in exponential form: (154)^½ or (154)^0.5
Square Root of 154 in radical form: √154

Square Root of 154

1.	What is the Square Root of 154?
2.	How to find the Square Root of 154?
3.	Is the Square Root of 154 Irrational?
4.	FAQs

What is the Square Root of 154?

The square root of 154, (or root 154), is the number which when multiplied by itself gives the product as 154. Therefore, the square root of 154 = √154 = 12.409673645990857.

☛ Check: Square Root Calculator

How to Find Square Root of 154?

Square Root of 154 by Long Division Method

Value of √154 by Long Division Method

Explanation:

Forming pairs: 01 and 54
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 54, to the right of the remainder 0. The new dividend is now 54.
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 <= 54. After finding Z, together 2 and Z (2) form a new divisor 22 for the new dividend 54.
Divide 54 by 22 with the quotient as 2, giving the remainder = 54 - 22 × 2 = 54 - 44 = 10.
Now, let's find the decimal places after the quotient 12.
Bring down 00 to the right of this remainder 10. The new dividend is now 1000.
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 <= 1000. Together they form a new divisor (244) for the new dividend (1000).
Divide 1000 by 244 with the quotient as 4, giving the remainder = 1000 - 244 × 4 = 1000 - 976 = 24.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 154.

Therefore, the square root of 154 by long division method is 12.4 approximately.

Is Square Root of 154 Irrational?

The actual value of √154 is undetermined. The value of √154 up to 25 decimal places is 12.40967364599085659613324. Hence, the square root of 154 is an irrational number.

☛ Also Check:

Square Root of 29 - √29 = 5.38516
Square Root of 63 - √63 = 7.93725
Square Root of 8 - √8 = 2.82843
Square Root of 113 - √113 = 10.63015
Square Root of 52 - √52 = 7.21110
Square Root of 44 - √44 = 6.63325
Square Root of 76 - √76 = 8.71780

Square Root of 154 Solved Examples

Example 1: Solve the equation x² − 154 = 0

Solution:

x² - 154 = 0 i.e. x² = 154
x = ±√154
Since the value of the square root of 154 is 12.410,
⇒ x = +√154 or -√154 = 12.410 or -12.410.
Example 2: If the surface area of a cube is 924 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 = 924 in²
⇒ a = ±√154 in
Since length can't be negative,
⇒ a = √154
We know that the square root of 154 is 12.410.
⇒ a = 12.410 in
Example 3: If the surface area of a sphere is 616π in². Find the radius of the sphere.

Solution:

Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr² = 616π in²
⇒ r = ±√154 in
Since radius can't be negative,
⇒ r = √154
The square root of 154 is 12.410.
⇒ r = 12.410 in

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FAQs on the Square Root of 154

What is the Value of the Square Root of 154?

The square root of 154 is 12.40967.

Why is the Square Root of 154 an Irrational Number?

Upon prime factorizing 154 i.e. 2¹ × 7¹ × 11¹, 2 is in odd power. Therefore, the square root of 154 is irrational.

What is the Square Root of 154 in Simplest Radical Form?

We need to express 154 as the product of its prime factors i.e. 154 = 2 × 7 × 11. Therefore, as visible, the radical form of the square root of 154 cannot be simplified further. Therefore, the simplest radical form of the square root of 154 can be written as √154

What is the Square of the Square Root of 154?

The square of the square root of 154 is the number 154 itself i.e. (√154)² = (154)^2/2 = 154.

Is the number 154 a Perfect Square?

The prime factorization of 154 = 2¹ × 7¹ × 11¹. Here, the prime factor 2 is not in the pair. Therefore, 154 is not a perfect square.

What is the Value of 18 square root 154?

The square root of 154 is 12.410. Therefore, 18 √154 = 18 × 12.410 = 223.374.

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