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Square Root of 448

The square root of 448 is expressed as √448 in the radical form and as (448)^½ or (448)^0.5 in the exponent form. The square root of 448 rounded up to 6 decimal places is 21.166010. It is the positive solution of the equation x² = 448. We can express the square root of 448 in its lowest radical form as 8 √7.

Square Root of 448: 21.166010488516726
Square Root of 448 in exponential form: (448)^½ or (448)^0.5
Square Root of 448 in radical form: √448 or 8 √7

Square Root of 448

1.	What is the Square Root of 448?
2.	How to find the Square Root of 448?
3.	Is the Square Root of 448 Irrational?
4.	FAQs

What is the Square Root of 448?

The square root of 448, (or root 448), is the number which when multiplied by itself gives the product as 448. Therefore, the square root of 448 = √448 = 8 √7 = 21.166010488516726.

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How to Find Square Root of 448?

Square Root of 448 by Long Division Method

Value of √448 by Long Division Method

Explanation:

Forming pairs: 04 and 48
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 48, to the right of the remainder 0. The new dividend is now 48.
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 1) such that 4Z × Z <= 48. After finding Z, together 4 and Z (1) form a new divisor 41 for the new dividend 48.
Divide 48 by 41 with the quotient as 1, giving the remainder = 48 - 41 × 1 = 48 - 41 = 7.
Now, let's find the decimal places after the quotient 21.
Bring down 00 to the right of this remainder 7. The new dividend is now 700.
Add the last digit of quotient to divisor i.e. 1 + 41 = 42. To the right of 42, find a digit Z (which is 1) such that 42Z × Z <= 700. Together they form a new divisor (421) for the new dividend (700).
Divide 700 by 421 with the quotient as 1, giving the remainder = 700 - 421 × 1 = 700 - 421 = 279.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 448.

Therefore, the square root of 448 by long division method is 21.1 approximately.

Is Square Root of 448 Irrational?

The actual value of √448 is undetermined. The value of √448 up to 25 decimal places is 21.16601048851672472401293. Hence, the square root of 448 is an irrational number.

☛ Also Check:

Square Root of 56 - √56 = 7.48331
Square Root of 1024 - √1024 = 32
Square Root of 116 - √116 = 10.77033
Square Root of 29 - √29 = 5.38516
Square Root of 73 - √73 = 8.54400
Square Root of 361 - √361 = 19
Square Root of 51 - √51 = 7.14143

Square Root of 448 Solved Examples

Example 1: Solve the equation x² − 448 = 0

Solution:

x² - 448 = 0 i.e. x² = 448
x = ±√448
Since the value of the square root of 448 is 21.166,
⇒ x = +√448 or -√448 = 21.166 or -21.166.
Example 2: If the area of a circle is 448π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 448π in²
⇒ r = ±√448 in
Since radius can't be negative,
⇒ r = √448
The square root of 448 is 21.166.
⇒ r = 21.166 in
Example 3: If the surface area of a cube is 2688 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 = 2688 in²
⇒ a = ±√448 in
Since length can't be negative,
⇒ a = √448
We know that the square root of 448 is 21.166.
⇒ a = 21.166 in

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FAQs on the Square Root of 448

What is the Value of the Square Root of 448?

The square root of 448 is 21.16601.

Why is the Square Root of 448 an Irrational Number?

Upon prime factorizing 448 i.e. 2⁶ × 7¹, 7 is in odd power. Therefore, the square root of 448 is irrational.

What is the Square of the Square Root of 448?

The square of the square root of 448 is the number 448 itself i.e. (√448)² = (448)^2/2 = 448.

What is the Value of 10 square root 448?

The square root of 448 is 21.166. Therefore, 10 √448 = 10 × 21.166 = 211.660.

If the Square Root of 448 is 21.166. Find the Value of the Square Root of 4.48.

Let us represent √4.48 in p/q form i.e. √(448/100) = 4.48/10 = 2.117. Hence, the value of √4.48 = 2.117

Is the number 448 a Perfect Square?

The prime factorization of 448 = 2⁶ × 7¹. Here, the prime factor 7 is not in the pair. Therefore, 448 is not a perfect square.

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