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Square Root of 424

The square root of 424 is expressed as √424 in the radical form and as (424)^½ or (424)^0.5 in the exponent form. The square root of 424 rounded up to 8 decimal places is 20.59126028. It is the positive solution of the equation x² = 424. We can express the square root of 424 in its lowest radical form as 2 √106.

Square Root of 424: 20.591260281974
Square Root of 424 in exponential form: (424)^½ or (424)^0.5
Square Root of 424 in radical form: √424 or 2 √106

Square Root of 424

1.	What is the Square Root of 424?
2.	How to find the Square Root of 424?
3.	Is the Square Root of 424 Irrational?
4.	FAQs

What is the Square Root of 424?

The square root of 424, (or root 424), is the number which when multiplied by itself gives the product as 424. Therefore, the square root of 424 = √424 = 2 √106 = 20.591260281974.

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How to Find Square Root of 424?

Square Root of 424 by Long Division Method

Value of √424 by Long Division Method

Explanation:

Forming pairs: 04 and 24
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 24, to the right of the remainder 0. The new dividend is now 24.
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 <= 24. After finding Z, together 4 and Z (0) form a new divisor 40 for the new dividend 24.
Divide 24 by 40 with the quotient as 0, giving the remainder = 24 - 40 × 0 = 24 - 0 = 24.
Now, let's find the decimal places after the quotient 20.
Bring down 00 to the right of this remainder 24. The new dividend is now 2400.
Add the last digit of quotient to divisor i.e. 0 + 40 = 40. To the right of 40, find a digit Z (which is 5) such that 40Z × Z <= 2400. Together they form a new divisor (405) for the new dividend (2400).
Divide 2400 by 405 with the quotient as 5, giving the remainder = 2400 - 405 × 5 = 2400 - 2025 = 375.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 424.

Therefore, the square root of 424 by long division method is 20.5 approx.

Is Square Root of 424 Irrational?

The actual value of √424 is undetermined. The value of √424 up to 25 decimal places is 20.59126028197400063159474. Hence, the square root of 424 is an irrational number.

☛ Also Check:

Square Root of 106 - √106 = 10.29563
Square Root of 72 - √72 = 8.48528
Square Root of 60 - √60 = 7.74597
Square Root of 45 - √45 = 6.70820
Square Root of 90 - √90 = 9.48683
Square Root of 10 - √10 = 3.16228
Square Root of 324 - √324 = 18

Square Root of 424 Solved Examples

Example 1: Solve the equation x² − 424 = 0

Solution:

x² - 424 = 0 i.e. x² = 424
x = ±√424
Since the value of the square root of 424 is 20.591,
⇒ x = +√424 or -√424 = 20.591 or -20.591.
Example 2: If the surface area of a cube is 2544 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 = 2544 in²
⇒ a = ±√424 in
Since length can't be negative,
⇒ a = √424
We know that the square root of 424 is 20.591.
⇒ a = 20.591 in
Example 3: If the area of an equilateral triangle is 424√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 = 424√3 in²
⇒ a = ±√1696 in
Since length can't be negative,
⇒ a = √1696 = 2 √424
We know that the square root of 424 is 20.591.
⇒ a = 41.183 in

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FAQs on the Square Root of 424

What is the Value of the Square Root of 424?

The square root of 424 is 20.59126.

Why is the Square Root of 424 an Irrational Number?

Upon prime factorizing 424 i.e. 2³ × 53¹, 2 is in odd power. Therefore, the square root of 424 is irrational.

Is the number 424 a Perfect Square?

The prime factorization of 424 = 2³ × 53¹. Here, the prime factor 2 is not in the pair. Therefore, 424 is not a perfect square.

What is the Square Root of 424 in Simplest Radical Form?

We need to express 424 as the product of its prime factors i.e. 424 = 2 × 2 × 2 × 53. Therefore, √424 = √2 × 2 × 2 × 53 = 2 √106. Thus, the square root of 424 in the lowest radical form is 2 √106.

Evaluate 14 plus 4 square root 424

The given expression is 14 + 4 √424. We know that the square root of 424 is 20.591. Therefore, 14 + 4 √424 = 14 + 4 × 20.591 = 14 + 82.365 = 96.365

What is the Square Root of -424?

The square root of -424 is an imaginary number. It can be written as √-424 = √-1 × √424 = i √424 = 20.591i
where i = √-1 and it is called the imaginary unit.

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