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Square Root of 179

The square root of 179 is expressed as √179 in the radical form and as (179)^½ or (179)^0.5 in the exponent form. The square root of 179 rounded up to 7 decimal places is 13.3790882. It is the positive solution of the equation x² = 179.

Square Root of 179: 13.379088160259652
Square Root of 179 in exponential form: (179)^½ or (179)^0.5
Square Root of 179 in radical form: √179

Square Root of 179

1.	What is the Square Root of 179?
2.	How to find the Square Root of 179?
3.	Is the Square Root of 179 Irrational?
4.	FAQs

What is the Square Root of 179?

The square root of 179, (or root 179), is the number which when multiplied by itself gives the product as 179. Therefore, the square root of 179 = √179 = 13.379088160259652.

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How to Find Square Root of 179?

Square Root of 179 by Long Division Method

Value of √179 by Long Division Method

Explanation:

Forming pairs: 01 and 79
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 79, to the right of the remainder 0. The new dividend is now 79.
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 3) such that 2Z × Z <= 79. After finding Z, together 2 and Z (3) form a new divisor 23 for the new dividend 79.
Divide 79 by 23 with the quotient as 3, giving the remainder = 79 - 23 × 3 = 79 - 69 = 10.
Now, let's find the decimal places after the quotient 13.
Bring down 00 to the right of this remainder 10. The new dividend is now 1000.
Add the last digit of quotient to divisor i.e. 3 + 23 = 26. To the right of 26, find a digit Z (which is 3) such that 26Z × Z <= 1000. Together they form a new divisor (263) for the new dividend (1000).
Divide 1000 by 263 with the quotient as 3, giving the remainder = 1000 - 263 × 3 = 1000 - 789 = 211.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 179.

Therefore, the square root of 179 by long division method is 13.3 approximately.

Is Square Root of 179 Irrational?

The actual value of √179 is undetermined. The value of √179 up to 25 decimal places is 13.37908816025965201502688. Hence, the square root of 179 is an irrational number.

☛ Also Check:

Square Root of 61 - √61 = 7.81025
Square Root of 73 - √73 = 8.54400
Square Root of 14 - √14 = 3.74166
Square Root of 51 - √51 = 7.14143
Square Root of 324 - √324 = 18
Square Root of 625 - √625 = 25
Square Root of 125 - √125 = 11.18034

Square Root of 179 Solved Examples

Example 1: Solve the equation x² − 179 = 0

Solution:

x² - 179 = 0 i.e. x² = 179
x = ±√179
Since the value of the square root of 179 is 13.379,
⇒ x = +√179 or -√179 = 13.379 or -13.379.
Example 2: If the surface area of a cube is 1074 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 = 1074 in²
⇒ a = ±√179 in
Since length can't be negative,
⇒ a = √179
We know that the square root of 179 is 13.379.
⇒ a = 13.379 in
Example 3: If the area of an equilateral triangle is 179√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 = 179√3 in²
⇒ a = ±√716 in
Since length can't be negative,
⇒ a = √716 = 2 √179
We know that the square root of 179 is 13.379.
⇒ a = 26.758 in

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FAQs on the Square Root of 179

What is the Value of the Square Root of 179?

The square root of 179 is 13.37908.

Why is the Square Root of 179 an Irrational Number?

The number 179 is prime. This implies that the number 179 is pairless and is not in the power of 2. Therefore, the square root of 179 is irrational.

Evaluate 16 plus 6 square root 179

The given expression is 16 + 6 √179. We know that the square root of 179 is 13.379. Therefore, 16 + 6 √179 = 16 + 6 × 13.379 = 16 + 80.275 = 96.275

What is the Square Root of 179 in Simplest Radical Form?

The number 179 is a prime number. This implies that the number 179 is pairless and is not in the power of 2. Therefore, the radical form of square root of 179 cannot be simplified further.

What is the Square Root of -179?

The square root of -179 is an imaginary number. It can be written as √-179 = √-1 × √179 = i √179 = 13.379i
where i = √-1 and it is called the imaginary unit.

If the Square Root of 179 is 13.379. Find the Value of the Square Root of 1.79.

Let us represent √1.79 in p/q form i.e. √(179/100) = 1.79/10 = 1.338. Hence, the value of √1.79 = 1.338

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