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Square Root of 432

The square root of 432 is expressed as √432 in the radical form and as (432)^½ or (432)^0.5 in the exponent form. The square root of 432 rounded up to 5 decimal places is 20.78461. It is the positive solution of the equation x² = 432. We can express the square root of 432 in its lowest radical form as 12 √3.

Square Root of 432: 20.784609690826528
Square Root of 432 in exponential form: (432)^½ or (432)^0.5
Square Root of 432 in radical form: √432 or 12 √3

Square Root of 432

1.	What is the Square Root of 432?
2.	How to find the Square Root of 432?
3.	Is the Square Root of 432 Irrational?
4.	FAQs

What is the Square Root of 432?

The square root of 432, (or root 432), is the number which when multiplied by itself gives the product as 432. Therefore, the square root of 432 = √432 = 12 √3 = 20.784609690826528.

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How to Find Square Root of 432?

Square Root of 432 by Long Division Method

Value of √432 by Long Division Method

Explanation:

Forming pairs: 04 and 32
Find a number Y (2) such that whose square is <= 4. Now divide 04 by 2 with quotient as 2.
Bring down the next pair 32, to the right of the remainder 0. The new dividend is now 32.
Add the last digit of the quotient (2) to the divisor (2) i.e. 2 + 2 = 4. To the right of 4, find a digit Z (which is 0) such that 4Z × Z <= 32. After finding Z, together 4 and Z (0) form a new divisor 40 for the new dividend 32.
Divide 32 by 40 with the quotient as 0, giving the remainder = 32 - 40 × 0 = 32 - 0 = 32.
Now, let's find the decimal places after the quotient 20.
Bring down 00 to the right of this remainder 32. The new dividend is now 3200.
Add the last digit of quotient to divisor i.e. 0 + 40 = 40. To the right of 40, find a digit Z (which is 7) such that 40Z × Z <= 3200. Together they form a new divisor (407) for the new dividend (3200).
Divide 3200 by 407 with the quotient as 7, giving the remainder = 3200 - 407 × 7 = 3200 - 2849 = 351.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 432.

Therefore, the square root of 432 by long division method is 20.7 approximately.

Is Square Root of 432 Irrational?

The actual value of √432 is undetermined. The value of √432 up to 25 decimal places is 20.78460969082652752232936. Hence, the square root of 432 is an irrational number.

☛ Also Check:

Square Root of 1681 - √1681 = 41
Square Root of 8 - √8 = 2.82843
Square Root of 40 - √40 = 6.32456
Square Root of 98 - √98 = 9.89949
Square Root of 22 - √22 = 4.69042
Square Root of 26 - √26 = 5.09902
Square Root of 48 - √48 = 6.92820

Square Root of 432 Solved Examples

Example 1: Solve the equation x² − 432 = 0

Solution:

x² - 432 = 0 i.e. x² = 432
x = ±√432
Since the value of the square root of 432 is 20.785,
⇒ x = +√432 or -√432 = 20.785 or -20.785.
Example 2: If the surface area of a cube is 2592 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 = 2592 in²
⇒ a = ±√432 in
Since length can't be negative,
⇒ a = √432
We know that the square root of 432 is 20.785.
⇒ a = 20.785 in
Example 3: If the area of an equilateral triangle is 432√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 = 432√3 in²
⇒ a = ±√1728 in
Since length can't be negative,
⇒ a = √1728 = 2 √432
We know that the square root of 432 is 20.785.
⇒ a = 41.569 in

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FAQs on the Square Root of 432

What is the Value of the Square Root of 432?

The square root of 432 is 20.7846.

Why is the Square Root of 432 an Irrational Number?

Upon prime factorizing 432 i.e. 2⁴ × 3³, 3 is in odd power. Therefore, the square root of 432 is irrational.

What is the Square of the Square Root of 432?

The square of the square root of 432 is the number 432 itself i.e. (√432)² = (432)^2/2 = 432.

What is the Square Root of -432?

The square root of -432 is an imaginary number. It can be written as √-432 = √-1 × √432 = i √432 = 20.784i
where i = √-1 and it is called the imaginary unit.

If the Square Root of 432 is 20.785. Find the Value of the Square Root of 4.32.

Let us represent √4.32 in p/q form i.e. √(432/100) = 4.32/10 = 2.078. Hence, the value of √4.32 = 2.078

What is the Value of 12 square root 432?

The square root of 432 is 20.785. Therefore, 12 √432 = 12 × 20.785 = 249.415.

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