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Square Root of 126

The square root of 126 is expressed as √126 in the radical form and as (126)^½ or (126)^0.5 in the exponent form. The square root of 126 rounded up to 5 decimal places is 11.22497. It is the positive solution of the equation x² = 126. We can express the square root of 126 in its lowest radical form as 3 √14.

Square Root of 126: 11.224972160321824
Square Root of 126 in exponential form: (126)^½ or (126)^0.5
Square Root of 126 in radical form: √126 or 3 √14

Square Root of 126

1.	What is the Square Root of 126?
2.	How to find the Square Root of 126?
3.	Is the Square Root of 126 Irrational?
4.	FAQs

What is the Square Root of 126?

The square root of 126, (or root 126), is the number which when multiplied by itself gives the product as 126. Therefore, the square root of 126 = √126 = 3 √14 = 11.224972160321824.

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How to Find Square Root of 126?

Square Root of 126 by Long Division Method

Value of √126 by Long Division Method

Explanation:

Forming pairs: 01 and 26
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 26, to the right of the remainder 0. The new dividend is now 26.
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 1) such that 2Z × Z <= 26. After finding Z, together 2 and Z (1) form a new divisor 21 for the new dividend 26.
Divide 26 by 21 with the quotient as 1, giving the remainder = 26 - 21 × 1 = 26 - 21 = 5.
Now, let's find the decimal places after the quotient 11.
Bring down 00 to the right of this remainder 5. The new dividend is now 500.
Add the last digit of quotient to divisor i.e. 1 + 21 = 22. To the right of 22, find a digit Z (which is 2) such that 22Z × Z <= 500. Together they form a new divisor (222) for the new dividend (500).
Divide 500 by 222 with the quotient as 2, giving the remainder = 500 - 222 × 2 = 500 - 444 = 56.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 126.

Therefore, the square root of 126 by long division method is 11.2 approximately.

Is Square Root of 126 Irrational?

The actual value of √126 is undetermined. The value of √126 up to 25 decimal places is 11.22497216032182415675125. Hence, the square root of 126 is an irrational number.

☛ Also Check:

Square Root of 23 - √23 = 4.79583
Square Root of 1681 - √1681 = 41
Square Root of 37 - √37 = 6.08276
Square Root of 69 - √69 = 8.30662
Square Root of 240 - √240 = 15.49193
Square Root of 96 - √96 = 9.79796
Square Root of 28 - √28 = 5.29150

Square Root of 126 Solved Examples

Example 1: Solve the equation x² − 126 = 0

Solution:

x² - 126 = 0 i.e. x² = 126
x = ±√126
Since the value of the square root of 126 is 11.225,
⇒ x = +√126 or -√126 = 11.225 or -11.225.
Example 2: If the area of a square is 126 in². Find the length of the side of the square.

Solution:

Let 'a' be the length of the side of the square.
⇒ Area of the square = a² = 126 in²
⇒ a = ±√126 in
Since length can't be negative,
⇒ a = √126 = 11.225 in
Example 3: If the area of an equilateral triangle is 126√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 = 126√3 in²
⇒ a = ±√504 in
Since length can't be negative,
⇒ a = √504 = 2 √126
We know that the square root of 126 is 11.225.
⇒ a = 22.450 in

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FAQs on the Square Root of 126

What is the Value of the Square Root of 126?

The square root of 126 is 11.22497.

Why is the Square Root of 126 an Irrational Number?

Upon prime factorizing 126 i.e. 2¹ × 3² × 7¹, 2 is in odd power. Therefore, the square root of 126 is irrational.

What is the Value of 3 square root 126?

The square root of 126 is 11.225. Therefore, 3 √126 = 3 × 11.225 = 33.675.

What is the Square Root of 126 in Simplest Radical Form?

We need to express 126 as the product of its prime factors i.e. 126 = 2 × 3 × 3 × 7. Therefore, √126 = √2 × 3 × 3 × 7 = 3 √14. Thus, the square root of 126 in the lowest radical form is 3 √14.

Is the number 126 a Perfect Square?

The prime factorization of 126 = 2¹ × 3² × 7¹. Here, the prime factor 2 is not in the pair. Therefore, 126 is not a perfect square.

Evaluate 17 plus 3 square root 126

The given expression is 17 + 3 √126. We know that the square root of 126 is 11.225. Therefore, 17 + 3 √126 = 17 + 3 × 11.225 = 17 + 33.675 = 50.675

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