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Square Root of 248

The square root of 248 is expressed as √248 in the radical form and as (248)^½ or (248)^0.5 in the exponent form. The square root of 248 rounded up to 6 decimal places is 15.748016. It is the positive solution of the equation x² = 248. We can express the square root of 248 in its lowest radical form as 2 √62.

Square Root of 248: 15.748015748023622
Square Root of 248 in exponential form: (248)^½ or (248)^0.5
Square Root of 248 in radical form: √248 or 2 √62

Square Root of 248

1.	What is the Square Root of 248?
2.	How to find the Square Root of 248?
3.	Is the Square Root of 248 Irrational?
4.	FAQs

What is the Square Root of 248?

The square root of 248, (or root 248), is the number which when multiplied by itself gives the product as 248. Therefore, the square root of 248 = √248 = 2 √62 = 15.748015748023622.

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How to Find Square Root of 248?

Square Root of 248 by Long Division Method

Value of √248 by Long Division Method

Explanation:

Forming pairs: 02 and 48
Find a number Y (1) such that whose square is <= 2. Now divide 02 by 1 with quotient as 1.
Bring down the next pair 48, to the right of the remainder 1. The new dividend is now 148.
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 5) such that 2Z × Z <= 148. After finding Z, together 2 and Z (5) form a new divisor 25 for the new dividend 148.
Divide 148 by 25 with the quotient as 5, giving the remainder = 148 - 25 × 5 = 148 - 125 = 23.
Now, let's find the decimal places after the quotient 15.
Bring down 00 to the right of this remainder 23. The new dividend is now 2300.
Add the last digit of quotient to divisor i.e. 5 + 25 = 30. To the right of 30, find a digit Z (which is 7) such that 30Z × Z <= 2300. Together they form a new divisor (307) for the new dividend (2300).
Divide 2300 by 307 with the quotient as 7, giving the remainder = 2300 - 307 × 7 = 2300 - 2149 = 151.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 248.

Therefore, the square root of 248 by long division method is 15.7 approximately.

Is Square Root of 248 Irrational?

The actual value of √248 is undetermined. The value of √248 up to 25 decimal places is 15.74801574802362203937007. Hence, the square root of 248 is an irrational number.

☛ Also Check:

Square Root of 320 - √320 = 17.88854
Square Root of 85 - √85 = 9.21954
Square Root of 26 - √26 = 5.09902
Square Root of 324 - √324 = 18
Square Root of 676 - √676 = 26
Square Root of 22 - √22 = 4.69042
Square Root of 97 - √97 = 9.84886

Square Root of 248 Solved Examples

Example 1: Solve the equation x² − 248 = 0

Solution:

x² - 248 = 0 i.e. x² = 248
x = ±√248
Since the value of the square root of 248 is 15.748,
⇒ x = +√248 or -√248 = 15.748 or -15.748.
Example 2: If the area of an equilateral triangle is 248√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 = 248√3 in²
⇒ a = ±√992 in
Since length can't be negative,
⇒ a = √992 = 2 √248
We know that the square root of 248 is 15.748.
⇒ a = 31.496 in
Example 3: If the area of a circle is 248π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 248π in²
⇒ r = ±√248 in
Since radius can't be negative,
⇒ r = √248
The square root of 248 is 15.748.
⇒ r = 15.748 in

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FAQs on the Square Root of 248

What is the Value of the Square Root of 248?

The square root of 248 is 15.74801.

Why is the Square Root of 248 an Irrational Number?

Upon prime factorizing 248 i.e. 2³ × 31¹, 2 is in odd power. Therefore, the square root of 248 is irrational.

What is the Square Root of 248 in Simplest Radical Form?

We need to express 248 as the product of its prime factors i.e. 248 = 2 × 2 × 2 × 31. Therefore, √248 = √2 × 2 × 2 × 31 = 2 √62. Thus, the square root of 248 in the lowest radical form is 2 √62.

If the Square Root of 248 is 15.748. Find the Value of the Square Root of 2.48.

Let us represent √2.48 in p/q form i.e. √(248/100) = 2.48/10 = 1.575. Hence, the value of √2.48 = 1.575

Is the number 248 a Perfect Square?

The prime factorization of 248 = 2³ × 31¹. Here, the prime factor 2 is not in the pair. Therefore, 248 is not a perfect square.

What is the Value of 5 square root 248?

The square root of 248 is 15.748. Therefore, 5 √248 = 5 × 15.748 = 78.740.

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